# LPTMS Publications

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## Two-fluid coexistence in a spinless fermions chain with pair hopping – Archive ouverte HAL

### Lorenzo Gotta

^{1}Leonardo Mazza^{1}Pascal Simon^{2}Guillaume Roux^{1}#### Lorenzo Gotta, Leonardo Mazza, Pascal Simon, Guillaume Roux. Two-fluid coexistence in a spinless fermions chain with pair hopping.

*Phys.Rev.Lett.*, 2021, 126 (20), pp.206805. ⟨10.1103/PhysRevLett.126.206805⟩. ⟨hal-03115808⟩We show that a simple one-dimensional model of spinless fermions with pair hopping displays a phase in which a Luttinger liquid of paired fermions coexists with a Luttinger liquid of unpaired fermions. Our results are based on extensive numerical density-matrix renormalization-group calculations and are supported by a two-fluid model that captures the essence of the coexistence region.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Tracy-Widom Distributions for the Gaussian Orthogonal and Symplectic Ensembles Revisited: A Skew-Orthogonal Polynomials Approach – Archive ouverte HAL

### Anthony Mays

^{1}Anita Ponsaing^{2}Grégory Schehr^{3}#### Anthony Mays, Anita Ponsaing, Grégory Schehr. Tracy-Widom Distributions for the Gaussian Orthogonal and Symplectic Ensembles Revisited: A Skew-Orthogonal Polynomials Approach.

*Journal of Statistical Physics*, Springer Verlag, 2021, 182 (2), ⟨10.1007/s10955-020-02695-w⟩. ⟨hal-03177663⟩We study the distribution of the largest eigenvalue in the "Pfaffian" classical ensembles of random matrix theory, namely in the Gaussian orthogonal (GOE) and Gaussian symplectic (GSE) ensembles, using semi-classical skew-orthogonal polynomials, in analogue to the approach of Nadal and Majumdar (NM) for the Gaussian unitary ensemble (GUE). Generalizing the techniques of Adler, Forrester, Nagao and van Moerbeke, and using "overlapping Pfaffian" identities due to Knuth, we explicitly construct these semi-classical skew-orthogonal polynomials in terms of the semi-classical orthogonal polynomials studied by NM in the case of the GUE. With these polynomials we obtain expressions for the cumulative distribution functions of the largest eigenvalue in the GOE and the GSE. Further, by performing asymptotic analysis of these skew-orthogonal polynomials in the limit of large matrix size, we obtain an alternative derivation of the Tracy-Widom distributions for GOE and GSE. This asymptotic analysis relies on a certain Pfaffian identity, the proof of which employs the characterization of Pfaffians in terms of perfect matchings and link diagrams.

- 1. University of Melbourne
- 2. University of Adelaide
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges – Archive ouverte HAL

### Lenart Zadnik

^{1}Kemal Bidzhiev^{1}Maurizio Fagotti^{1}#### Lenart Zadnik, Kemal Bidzhiev, Maurizio Fagotti. The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges.

*SciPost Phys.*, 2021, 10, pp.099. ⟨10.21468/SciPostPhys.10.5.099⟩. ⟨hal-03022690⟩We study the (dual) folded spin-1/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of local macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization – Archive ouverte HAL

### A. Bilen

^{1}Bertrand Georgeot^{2}O. Giraud^{3}Gabriel Lemarié^{2, 4, 5}I. García-Mata^{1}#### A. Bilen, Bertrand Georgeot, O. Giraud, Gabriel Lemarié, I. García-Mata. Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization.

*Physical Review Research*, American Physical Society, 2021, 3, pp.L022023. ⟨hal-03160414⟩Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension $\Delta_q$ is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation \mbox{$\Delta_q=\Delta_{1-q}$} is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that the reason for this is the presence of atypically small eigenfunction amplitudes induced by two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.

- 1. IFIMAR - Instituto de Investigaciones Físicas de Mar del Plata
- 2. LPT - Laboratoire de Physique Théorique
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. UMI 3654 - MajuLab
- 5. CQT - Centre for Quantum Technologies [Singapore]

## Survival probability of a run-and-tumble particle in the presence of a drift – Archive ouverte HAL

### Benjamin de Bruyne

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}#### Benjamin de Bruyne, Satya N. Majumdar, Gregory Schehr. Survival probability of a run-and-tumble particle in the presence of a drift.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03223973⟩We consider a one-dimensional run-and-tumble particle, or persistent random walk, in the presence of an absorbing boundary located at the origin. After each tumbling event, which occurs at a constant rate $\gamma$, the (new) velocity of the particle is drawn randomly from a distribution $W(v)$. We study the survival probability $S(x,t)$ of a particle starting from $x \geq 0$ up to time $t$ and obtain an explicit expression for its double Laplace transform (with respect to both $x$ and $t$) for an arbitrary velocity distribution $W(v)$, not necessarily symmetric. This result is obtained as a consequence of Spitzer's formula, which is well known in the theory of random walks and can be viewed as a generalization of the Sparre Andersen theorem. We then apply this general result to the specific case of a two-state particle with velocity $\pm v_0$, the so-called persistent random walk (PRW), and in the presence of a constant drift $\mu$ and obtain an explicit expression for $S(x,t)$, for which we present more detailed results. Depending on the drift $\mu$, we find a rich variety of behaviours for $S(x,t)$, leading to three distinct cases: (i) subcritical drift $-v_0\!<\!\mu\!<\! v_0$, (ii) supercritical drift $\mu < -v_0$ and (iii) critical drift $\mu=-v_0$. In these three cases, we obtain exact analytical expressions for the survival probability $S(x,t)$ and establish connections with existing formulae in the mathematics literature. Finally, we discuss some applications of these results to record statistics and to the statistics of last-passage times.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Surfing on minima of isostatic landscapes: avalanches and unjamming transition – Archive ouverte HAL

### Silvio Franz

^{1}Antonio Sclocchi^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Surfing on minima of isostatic landscapes: avalanches and unjamming transition.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03223882⟩Recently, we showed that optimization problems, both in infinite as well as in finite dimensions, for continuous variables and soft excluded volume constraints, can display entire isostatic phases where local minima of the cost function are marginally stable configurations endowed with non-linear excitations [1,2]. In this work we describe an athermal adiabatic algorithm to explore with continuity the corresponding rough high-dimensional landscape. We concentrate on a prototype problem of this kind, the spherical perceptron optimization problem with linear cost function (hinge loss). This algorithm allows to "surf" between isostatic marginally stable configurations and to investigate some properties of such landscape. In particular we focus on the statistics of avalanches occurring when local minima are destabilized. We show that when perturbing such minima, the system undergoes plastic rearrangements whose size is power law distributed and we characterize the corresponding critical exponent. Finally we investigate the critical properties of the unjamming transition, showing that the linear interaction potential gives rise to logarithmic behavior in the scaling of energy and pressure as a function of the distance from the unjamming point. For some quantities, the logarithmic corrections can be gauged out. This is the case of the number of soft constraints that are violated as a function of the distance from jamming which follows a non-trivial power law behavior.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Supersolidity of cnoidal waves in an ultracold Bose gas – Archive ouverte HAL

### Giovanni I. MartoneAlessio RecatiNicolas Pavloff

^{1}#### Giovanni I. Martone, Alessio Recati, Nicolas Pavloff. Supersolidity of cnoidal waves in an ultracold Bose gas.

*Physical Review Research*, American Physical Society, 2021, 3 (1), ⟨10.1103/PhysRevResearch.3.013143⟩. ⟨hal-03223891⟩A one-dimensional Bose-Einstein condensate may experience nonlinear periodic modulations known as "cnoidal waves". We argue that such structures represent promising candidates for the study of supersolidity-related phenomena in a non-equilibrium state. A mean-field treatment makes it possible to rederive Leggett's formula for the superfluid fraction of the system and to estimate it analytically. We determine the excitation spectrum, for which we obtain analytical results in the two opposite limiting cases of (i) a linearly modulated background and (ii) a train of dark solitons. The presence of two Goldstone (gapless) modes -- associated with the spontaneous breaking of $\mathrm{U}(1)$ symmetry and of continuous translational invariance -- at large wavelength is verified. We also calculate the static structure factor and the compressibility of cnoidal waves, which show a divergent behavior at the edges of each Brillouin zone.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Statistical properties of structured random matrices – Archive ouverte HAL

### Eugene Bogomolny

^{1}Olivier Giraud^{1}#### Eugene Bogomolny, Olivier Giraud. Statistical properties of structured random matrices.

*Physical Review E*, American Physical Society (APS), 2021, 103 (4), ⟨10.1103/PhysRevE.103.042213⟩. ⟨hal-03223965⟩Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral statistics of all these random matrices is of intermediate type, characterized by (i) level repulsion at small distances, (ii) an exponential decrease of the nearest-neighbor distributions at large distances, (iii) a non-trivial value of the spectral compressibility, and (iv) the existence of non-trivial fractal dimensions of eigenvectors in Fourier space. Our findings show that intermediate-type statistics is more ubiquitous and universal than was considered so far and open a new direction in random matrix theory.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions – Archive ouverte HAL

### Clément Le PriolPierre Le Doussal

^{1}Alberto Rosso^{2}#### Clément Le Priol, Pierre Le Doussal, Alberto Rosso. Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions.

*Physical Review Letters*, American Physical Society, 2021, 126 (2), ⟨10.1103/PhysRevLett.126.025702⟩. ⟨hal-03117974⟩Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this paper we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaym{\'e}-Galton-Watson process describing the statistics of the cluster number. Our work has a concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Self-induced glassy phase in multimodal cavity quantum electrodynamics – Archive ouverte HAL

### Vittorio ErbaMauro Pastore

^{1}Pietro Rotondo#### Vittorio Erba, Mauro Pastore, Pietro Rotondo. Self-induced glassy phase in multimodal cavity quantum electrodynamics.

*Physical Review Letters*, American Physical Society, 2021. ⟨hal-03223947⟩We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both non-local and non-translational invariant, and randomness in the atoms positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting where atoms form a one-dimensional regular chain and we study the thermodynamics of the resulting effective Ising model. We present extensive results showing that the system has a low-temperature glassy phase. Notably, for rational values of the only free adimensional parameter $\alpha=p/q$ of the interaction, the number of metastable states at low temperature grows exponentially with $q$ and the problem of finding the ground state rapidly becomes computationally intractable, suggesting that the system develops high energy barriers and ergodicity breaking occurs.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Proliferation of non-linear excitations in the piecewise-linear perceptron – Archive ouverte HAL

### Antonio Sclocchi

^{1}Pierfrancesco Urbani^{2}#### Antonio Sclocchi, Pierfrancesco Urbani. Proliferation of non-linear excitations in the piecewise-linear perceptron.

*SciPost Physics*, SciPost Foundation, 2021. ⟨hal-03223926⟩We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable and displaying a set of pseudogaps, singularities and non-linear excitations whose properties appear to be in the same universality class of jammed packings of hard spheres. The piecewise linear perceptron problem appears as an evolution of the purely linear perceptron optimization problem that has been recently investigated in [1]. Its cost function contains two non-analytic points where the derivative has a jump. Correspondingly, in the non-convex/glassy phase, these two points give rise to four pseudogaps in the force distribution and this induces four power laws in the gap distribution as well. In addition one can define an extended notion of isostaticity and show that local minima appear again to be isostatic in this phase. We believe that our results generalize naturally to more complex cases with a proliferation of non-linear excitations as the number of non-analytic points in the cost function is increased.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Position distribution in a generalized run-and-tumble process – Archive ouverte HAL

### David S. Dean

^{1}Satya N. Majumdar^{2}Hendrik Schawe#### David S. Dean, Satya N. Majumdar, Hendrik Schawe. Position distribution in a generalized run-and-tumble process.

*Physical Review E*, American Physical Society (APS), 2021, 103 (1), ⟨10.1103/PhysRevE.103.012130⟩. ⟨hal-03223889⟩We study a class of stochastic processes of the type $\frac{d^n x}{dt^n}= v_0\, \sigma(t)$ where $n>0$ is a positive integer and $\sigma(t)=\pm 1$ represents an `active' telegraphic noise that flips from one state to the other with a constant rate $\gamma$. For $n=1$, it reduces to the standard run and tumble process for active particles in one dimension. This process can be analytically continued to any $n>0$ including non-integer values. We compute exactly the mean squared displacement at time $t$ for all $n>0$ and show that at late times while it grows as $\sim t^{2n-1}$ for $n>1/2$, it approaches a constant for $n<1/2$. In the marginal case $n=1/2$, it grows very slowly with time as $\sim \ln t$. Thus the process undergoes a {\em localisation} transition at $n=1/2$. We also show that the position distribution $p_n(x,t)$ remains time-dependent even at late times for $n\ge 1/2$, but approaches a stationary time-independent form for $n<1/2$. The tails of the position distribution at late times exhibit a large deviation form, $p_n(x,t)\sim \exp\left[-\gamma\, t\, \Phi_n\left(\frac{x}{x^*(t)}\right)\right]$, where $x^*(t)= v_0\, t^n/\Gamma(n+1)$. We compute the rate function $\Phi_n(z)$ analytically for all $n>0$ and also numerically using importance sampling methods, finding excellent agreement between them. For three special values $n=1$, $n=2$ and $n=1/2$ we compute the exact cumulant generating function of the position distribution at all times $t$.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Phase slips, dislocations, half-integer vortices, two-fluid hydrodynamics and the chiral anomaly in charge and spin density waves – Archive ouverte HAL

### Serguei Brazovskii

^{1}Natasha Kirova^{2}#### Serguei Brazovskii, Natasha Kirova. Phase slips, dislocations, half-integer vortices, two-fluid hydrodynamics and the chiral anomaly in charge and spin density waves.

*J.Exp.Theor.Phys.*, 2021, 132 (4), pp.714-726. ⟨10.1134/S1063776121040038⟩. ⟨hal-03178611⟩This brief review recalls some chapters in theory of sliding incommensurate density waves which may have appeared after inspirations from studies of Dzyaloshinskii and collaborations with him. First we address the spin density waves which rich order parameter allows for an unusual object of a complex topological nature: a half-integer dislocation combined with a semi-vortex of the staggered magnetization. It becomes energetically preferable with respect to an ordinary dislocation due to the high Coulomb energy at low concentration of carriers. Generation of these objects should form a sequence of π-phase slips in accordance with experimental doubling of the phase-slips rate. Next, we revise the commonly employed TDGL approach which is shown to suffer from a violation of the charge conservation law resulting in nonphysical generation of particles which is particularly pronounced for electronic vortices in the course of their nucleation or motion. The suggested consistent theory exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The derived equations clarify partitions of charges, currents, and rigidity among subsystems of condensed and normal carriers and the gluing electric field. Being non-analytical with respect to the order parameter, contrarily the conventional TDGL type, the resulting equations still allow for a numerical modeling of transient processes related to space- and spatiotemporal vorticity in DWs.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Pairing in spinless fermions and spin chains with next-nearest neighbor interactions – Archive ouverte HAL

### Lorenzo Gotta

^{1}Leonardo Mazza^{1}Pascal Simon^{2}Guillaume Roux^{1}#### Lorenzo Gotta, Leonardo Mazza, Pascal Simon, Guillaume Roux. Pairing in spinless fermions and spin chains with next-nearest neighbor interactions.

*Physical Review Research*, American Physical Society, 2021, 3 (1), ⟨10.1103/PhysRevResearch.3.013114⟩. ⟨hal-03177638⟩We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest neighbour range. In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbour and next-nearest-neighbour interactions. Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations. The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles. In relation with recent studies, we show several emergent transition lines with a central charge $c = 3/2$ between the Luttinger-liquid and the cluster Luttinger liquid phases. These results could be experimentally investigated using highly-tunable quantum simulators.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Optimization and Growth in First-Passage Resetting – Archive ouverte HAL

### B. de Bruyne

^{1}J. Randon-FurlingS. Redner#### B. de Bruyne, J. Randon-Furling, S. Redner. Optimization and Growth in First-Passage Resetting.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03117919⟩We combine the processes of resetting and first-passage to define \emph{first-passage resetting}, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. In an infinite domain, first-passage resetting of isotropic diffusion is non-stationary, with the number of resetting events growing with time as $\sqrt{t}$. We calculate the resulting spatial probability distribution of the particle analytically, and also obtain this distribution by a geometric path decomposition. In a finite interval, we define an optimization problem that is controlled by first-passage resetting; this scenario is motivated by reliability theory. The goal is to operate a system close to its maximum capacity without experiencing too many breakdowns. However, when a breakdown occurs the system is reset to its minimal operating point. We define and optimize an objective function that maximizes the reward (being close to maximum operation) minus a penalty for each breakdown. We also investigate extensions of this basic model to include delay after each reset and to two dimensions. Finally, we study the growth dynamics of a domain in which the domain boundary recedes by a specified amount whenever the diffusing particle reaches the boundary after which a resetting event occurs. We determine the growth rate of the domain for the semi-infinite line and the finite interval and find a wide range of behaviors that depend on how much the recession occurs when the particle hits the boundary.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## One-dimensional colloidal model with dielectric inhomogeneity – Archive ouverte HAL

### Lucas Varela

^{1}Gabriel TéllezEmmanuel Trizac^{1}#### Lucas Varela, Gabriel Téllez, Emmanuel Trizac. One-dimensional colloidal model with dielectric inhomogeneity.

*Physical Review E*, American Physical Society (APS), 2021, 103 (4), ⟨10.1103/PhysRevE.103.042603⟩. ⟨hal-03223979⟩We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counter-ions ($N$) being even. The results are shown to recover the mean-field prediction in the limit $N\to \infty$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## On non-canonical degrees of freedom – Archive ouverte HAL

### Eoin Quinn

^{1}#### Eoin Quinn. On non-canonical degrees of freedom.

*SciPost Phys.*, 2021, 10, pp.075. ⟨10.21468/SciPostPhys.10.3.075⟩. ⟨hal-02973159⟩Non-canonical degrees of freedom provide one of the most promising routes towards characterising a range of important phenomena in condensed matter physics. Potential candidates include the pseudogap regime of the cuprates, heavy-fermion behaviour, and also indeed magnetically ordered systems. Nevertheless it remains an open question whether non-canonical algebras can in fact provide legitimate quantum degrees of freedom. In this manuscript we survey progress made on this topic, complementing distinct approaches so as to obtain a unified description. In particular we obtain a novel closed-form expression for a self-energy-like object for non-canonical degrees of freedom. We further make a resummation of density correlations to obtain analogues of the RPA and GW approximations commonly employed for canonical degrees of freedom. We discuss difficulties related to generating higher-order approximations which are consistent with conservation laws, which represents an outstanding issue. We also discuss how the interplay between canonical and non-canonical degrees of freedom offers a useful paradigm for organising the phase diagram of correlated electronic behaviour.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Non-intersecting Brownian Bridges in the Flat-to-Flat Geometry – Archive ouverte HAL

### Jacek GrelaSatya N. Majumdar

^{1}Grégory Schehr^{2}#### Jacek Grela, Satya N. Majumdar, Grégory Schehr. Non-intersecting Brownian Bridges in the Flat-to-Flat Geometry.

*J.Statist.Phys.*, 2021, 183 (3), pp.49. ⟨10.1007/s10955-021-02774-6⟩. ⟨hal-03260827⟩We study N vicious Brownian bridges propagating from an initial configuration $\{a_1< a_2< \ldots < a_N \}$ at time $t=0$ to a final configuration $\{b_1< b_2< \ldots < b_N \}$ at time $t=t_f$, while staying non-intersecting for all $0\le t \le t_f$. We first show that this problem can be mapped to a non-intersecting Dyson’s Brownian bridges with Dyson index $\beta =2$. For the latter we derive an exact effective Langevin equation that allows to generate very efficiently the vicious bridge configurations. In particular, for the flat-to-flat configuration in the large N limit, where $a_i = b_i = (i-1)/N$, for $i = 1, \ldots , N$, we use this effective Langevin equation to derive an exact Burgers’ equation (in the inviscid limit) for the Green’s function and solve this Burgers’ equation for arbitrary time $0 \le t\le t_f$. At certain specific values of intermediate times t, such as $t=t_f/2$, $t=t_f/3$ and $t=t_f/4$ we obtain the average density of the flat-to-flat bridge explicitly. We also derive explicitly how the two edges of the average density evolve from time $t=0$ to time $t=t_f$. Finally, we discuss connections to some well known problems, such as the Chern–Simons model, the related Stieltjes–Wigert orthogonal polynomials and the Borodin–Muttalib ensemble of determinantal point processes.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies

## Non-canonical degrees of freedom – Archive ouverte HAL

### Eoin Quinn

^{1}#### Eoin Quinn. Non-canonical degrees of freedom.

*SciPost Phys.*, 2021, 10, pp.075. ⟨10.21468/SciPostPhys.10.3.075⟩. ⟨hal-02973159⟩Non-canonical degrees of freedom provide one of the most promising routes towards characterising a range of important phenomena in condensed matter physics. Potential candidates include the pseudogap regime of the cuprates, heavy-fermion behaviour, and also indeed magnetically ordered systems. Nevertheless it remains an open question whether non-canonical algebras can in fact provide legitimate quantum degrees of freedom. In this manuscript we survey progress made on this topic, complementing distinct approaches so as to obtain a unified description. In particular we obtain a novel closed-form expression for a self-energy-like object for non-canonical degrees of freedom. We further make a resummation of density correlations to obtain analogues of the RPA and GW approximations commonly employed for canonical degrees of freedom. We discuss difficulties related to generating higher-order approximations which are consistent with conservation laws, which represents an outstanding issue. We also discuss how the interplay between canonical and non-canonical degrees of freedom offers a useful paradigm for organising the phase diagram of correlated electronic behaviour.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Neutral theory for competing attention in social networks – Archive ouverte HAL

### Carlos A. Plata

^{1, 2}Emanuele Pigani^{2}Sandro Azaele^{2}María J. PalazziAlbert Solé-RibaltaSandro MeloniJavier Borge-HolthoeferSamir Suweis^{2}Violeta Calleja-Solanas#### Carlos A. Plata, Emanuele Pigani, Sandro Azaele, María J. Palazzi, Albert Solé-Ribalta, et al.. Neutral theory for competing attention in social networks.

*Physical Review Research*, American Physical Society, 2021, 3 (1), ⟨10.1103/PhysRevResearch.3.013070⟩. ⟨hal-03180557⟩We used an ecological approach based on a neutral model to study the competition for attention in an online social network. This novel approach allow us to analyze some ecological patterns that has also an insightful meaning in the context of information ecosystem. Specifically, we focus on the study of patterns related with the persistence of a meme within the network and the capacity of the system to sustain coexisting memes. Not only are we able of doing such analysis in an approximated continuum limit, but also we get exact results of the finite-size discrete system.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica [Padova]

## Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap – Archive ouverte HAL

### Manas Kulkarni

^{1}Satya N. Majumdar^{2}Grégory Schehr^{2}#### Manas Kulkarni, Satya N. Majumdar, Grégory Schehr. Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap.

*Physical Review A*, American Physical Society 2021, 103 (3), ⟨10.1103/PhysRevA.103.033321⟩. ⟨hal-03179775⟩We compute exactly the average spatial density for $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\Omega$ in the presence of an additional repulsive central potential $\gamma/r^2$. We find that, in the large $N$ limit, the bulk density has a rich and nontrivial profile -- with a hole at the center of the trap and surrounded by a multi-layered "wedding cake" structure. The number of layers depends on $N$ and on the two parameters $\Omega$ and $\gamma$ leading to a rich phase diagram. Zooming in on the edge of the $k^{\rm th}$ layer, we find that the edge density profile exhibits $k$ kinks located at the zeroes of the $k^{\rm th}$ Hermite polynomial. Interestingly, in the large $k$ limit, we show that the edge density profile approaches a limiting form, which resembles the shape of a propagating front, found in the unitary evolution of certain quantum spin chains. We also study how a newly formed droplet grows in size on top of the last layer as one changes the parameters.

- 1. ICTS-TIFR - International Centre for Theoretical Sciences [TIFR]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Mixed Bubbles in Bose-Bose Mixtures – Archive ouverte HAL

### P. NaidonD. s. Petrov

^{1}#### P. Naidon, D. s. Petrov. Mixed Bubbles in Bose-Bose Mixtures.

*Physical Review Letters*, American Physical Society, 2021, 126 (11), ⟨10.1103/PhysRevLett.126.115301⟩. ⟨hal-03223902⟩Repulsive Bose-Bose mixtures are known to either mix or phase-separate into pure components. Here we predict a mixed-bubble regime in which bubbles of the mixed phase coexist with a pure phase of one of the components. This is a beyond-mean-field effect which occurs for unequal masses or unequal intraspecies coupling constants and is due to a competition between the mean-field term, quadratic in densities, and a nonquadratic beyond-mean-field correction. We find parameters of the mixed-bubble regime in all dimensions and discuss implications for current experiments.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting – Archive ouverte HAL

### Satya N. Majumdar

^{1}Francesco Mori^{1}Hendrik Schawe^{2}Grégory Schehr^{1}#### Satya N. Majumdar, Francesco Mori, Hendrik Schawe, Grégory Schehr. Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting.

*Physical Review E*, American Physical Society (APS), 2021, 103 (2), ⟨10.1103/PhysRevE.103.022135⟩. ⟨hal-03177642⟩We compute exactly the mean perimeter and the mean area of the convex hull of a $2$-d Brownian motion of duration $t$ and diffusion constant $D$, in the presence of resetting to the origin at a constant rate $r$. We show that for any $t$, the mean perimeter is given by $\langle L(t)\rangle= 2 \pi \sqrt{\frac{D}{r}}\, f_1(rt)$ and the mean area is given by $\langle A(t) \rangle= 2\pi\frac{D}{r}\, f_2(rt)$ where the scaling functions $f_1(z)$ and $f_2(z)$ are computed explicitly. For large $t\gg 1/r$, the mean perimeter grows extremely slowly as $\langle L(t)\rangle \propto \ln (rt)$ with time. Likewise, the mean area also grows slowly as $\langle A(t)\rangle \propto \ln^2(rt)$ for $t\gg 1/r$. Our exact results indicate that the convex hull, in the presence of resetting, approaches a circular shape at late times. Numerical simulations are in perfect agreement with our analytical predictions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

## Localization transition in the Discrete Non-Linear Schr\ »odinger Equation: ensembles inequivalence and negative temperatures – Archive ouverte HAL

### Giacomo GradenigoStefano IubiniRoberto LiviSatya N. Majumdar

^{1}#### Giacomo Gradenigo, Stefano Iubini, Roberto Livi, Satya N. Majumdar. Localization transition in the Discrete Non-Linear Schr\"odinger Equation: ensembles inequivalence and negative temperatures.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03223864⟩We present a detailed account of a first-order localization transition in the Discrete Nonlinear Schr\"odinger Equation, where the localized phase is associated to the high energy region in parameter space. We show that, due to ensemble inequivalence, this phase is thermodynamically stable only in the microcanonical ensemble. In particular, we obtain an explicit expression of the microcanonical entropy close to the transition line, located at infinite temperature. This task is accomplished making use of large-deviation techniques, that allow us to compute, in the limit of large system size, also the subleading corrections to the microcanonical entropy. These subleading terms are crucial ingredients to account for the first-order mechanism of the transition, to compute its order parameter and to predict the existence of negative temperatures in the localized phase. All of these features can be viewed as signatures of a thermodynamic phase where the translational symmetry is broken spontaneously due to a condensation mechanism yielding energy fluctuations far away from equipartition: actually they prefer to participate in the formation of nonlinear localized excitations (breathers), typically containing a macroscopic fraction of the total energy.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Level Set Percolation in the Two-Dimensional Gaussian Free Field – Archive ouverte HAL

### Xiangyu Cao

^{1}Raoul Santachiara^{2}#### Xiangyu Cao, Raoul Santachiara. Level Set Percolation in the Two-Dimensional Gaussian Free Field.

*Physical Review Letters*, American Physical Society, 2021, 126 (12), ⟨10.1103/PhysRevLett.126.120601⟩. ⟨hal-03176908⟩- 1. Systèmes Classiques ou Quantiques en Interaction
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Kernels for non interacting fermions via a Green’s function approach with applications to step potentials – Archive ouverte HAL

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Grégory Schehr^{2}Naftali R. Smith^{2}David Dean^{3}#### Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr, Naftali R. Smith, David Dean. Kernels for non interacting fermions via a Green’s function approach with applications to step potentials.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2021, 54 (8), pp.084001. ⟨10.1088/1751-8121/abd9ef⟩. ⟨hal-03177657⟩The quantum correlations of $N$ noninteracting spinless fermions in their ground state can be expressed in terms of a two-point function called the kernel. Here we develop a general and compact method for computing the kernel in a general trapping potential in terms of the Green's function for the corresponding single particle Schr\"odinger equation. For smooth potentials the method allows a simple alternative derivation of the local density approximation for the density and of the sine kernel in the bulk part of the trap in the large $N$ limit. It also recovers the density and the kernel of the so-called {\em Airy gas} at the edge. This method allows to analyse the quantum correlations in the ground state when the potential has a singular part with a fast variation in space. For the square step barrier of height $V_0$, we derive explicit expressions for the density and for the kernel. For large Fermi energy $\mu>V_0$ it describes the interpolation between two regions of different densities in a Fermi gas, each described by a different sine kernel. Of particular interest is the {\em critical point} of the square well potential when $\mu=V_0$. In this critical case, while there is a macroscopic number of fermions in the lower part of the step potential, there is only a finite $O(1)$ number of fermions on the shoulder, and moreover this number is independent of $\mu$. In particular, the density exhibits an algebraic decay $\sim 1/x^2$, where $x$ is the distance from the jump. Furthermore, we show that the critical behaviour around $\mu = V_0$ exhibits universality with respect with the shape of the barrier. This is established (i) by an exact solution for a smooth barrier (the Woods-Saxon potential) and (ii) by establishing a general relation between the large distance behavior of the kernel and the scattering amplitudes of the single-particle wave-function.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LOMA - Laboratoire Ondes et Matière d'Aquitaine

## Impurities in systems of noninteracting trapped fermions – Archive ouverte HAL

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Gregory Schehr^{3}#### David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr. Impurities in systems of noninteracting trapped fermions.

*SciPost Physics*, SciPost Foundation, 2021, 10 (4), ⟨10.21468/SciPostPhys.10.4.082⟩. ⟨hal-03223977⟩We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-Péché (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Higher-order effective interactions for bosons near a two-body zero crossing – Archive ouverte HAL

### A. Pricoupenko

^{1}D. S. Petrov^{1}#### A. Pricoupenko, D. S. Petrov. Higher-order effective interactions for bosons near a two-body zero crossing.

*Physical Review A*, American Physical Society 2021, 103 (3), ⟨10.1103/PhysRevA.103.033326⟩. ⟨hal-03223944⟩We develop the perturbation theory for bosons interacting via a two-body potential $V$ of vanishing mean value. We find that the leading nonpairwise contribution to the energy emerges in the third order in $V$ and represents an effective three-body interaction, the sign of which in most cases (although not in general) is anticorrelated with the sign of the long-range tail of $V$. Explicit results are obtained for a few particular two-body interaction potentials and we perform a detailed perturbative analysis of tilted dipoles in quasi-low-dimensional geometries.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Gradient descent dynamics in the mixed $p$-spin spherical model: finite size simulation and comparison with mean-field integration – Archive ouverte HAL

### Giampaolo Folena

^{1}Silvio Franz^{1}Federico Ricci-Tersenghi#### Giampaolo Folena, Silvio Franz, Federico Ricci-Tersenghi. Gradient descent dynamics in the mixed $p$-spin spherical model: finite size simulation and comparison with mean-field integration.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03223872⟩We perform numerical simulations of a long-range spherical spin glass with two and three body interaction terms. We study the gradient descent dynamics and the inherent structures found after a quench from initial conditions, well thermalized at temperature $T_{in}$. In large systems, the dynamics strictly agrees with the integration of the mean-field dynamical equations. In particular, we confirm the existence of an onset initial temperature, within the liquid phase, below which the energy of the inherent structures undoubtedly depends on $T_{in}$. This behavior is in contrast with that of pure models, where there is a 'threshold energy' that attracts all the initial configurations in the liquid. Our results strengthen the analogy between mean-field spin glass models and supercooled liquids.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## From One- to Two-Magnon Excitations in the S = 3 / 2 Magnet β − CaCr 2 O 4 – Archive ouverte HAL

### M. SongvilayS. PetitF. DamayG. Roux

^{1}N. QureshiH. c. WalkerJ. a. Rodriguez-RiveraB. GaoS. -W. CheongC. Stock#### M. Songvilay, S. Petit, F. Damay, G. Roux, N. Qureshi, et al.. From One- to Two-Magnon Excitations in the S = 3 / 2 Magnet β − CaCr 2 O 4.

*Physical Review Letters*, American Physical Society, 2021, 126 (1), ⟨10.1103/PhysRevLett.126.017201⟩. ⟨hal-03117938⟩We apply neutron spectroscopy to measure the magnetic dynamics in the S=3/2 magnet $\beta$-CaCr$_2$O$_4$ (T$_N$=21 K). The low-energy fluctuations, in the ordered state, resemble large-S linear spin-waves from the incommensurate ground state. However, at higher energy transfers, these semi-classical and harmonic dynamics are replaced by an energy and momentum broadened continuum of excitations. Applying kinematic constraints required for energy and momentum conservation, sum rules of neutron scattering, and comparison against exact diagonalization calculations, we show that the dynamics at high-energy transfers resemble low-S one-dimensional quantum fluctuations. $\beta$-CaCr$_2$O$_4$ represents an example of a magnet at the border between classical N\'eel and quantum phases, displaying dual characteristics.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Formation of superscar waves in plane polygonal billiards – Archive ouverte HAL

### Eugene Bogomolny

^{1}#### Eugene Bogomolny. Formation of superscar waves in plane polygonal billiards.

*Journal of Physics Communications*, IOP Publishing, 2021. ⟨hal-03262543⟩Polygonal billiards constitute a special class of models. Though they have zero Lyapunov exponent their classical and quantum properties are involved due to scattering on singular vertices. It is demonstrated that in the semiclassical limit multiple singular scattering on such vertices when optical boundaries of many scatters overlap leads to vanishing of quantum wave functions along straight lines built by these scatters. This phenomenon has an especially important consequence for polygonal billiards where periodic orbits (when they exist) form pencils of parallel rays restricted from the both sides by singular vertices. Due to singular scattering on boundary vertices, waves propagated inside periodic orbit pencils in the semiclassical limit tend to zero along pencil boundaries thus forming weakly interacting quasi-modes. Contrary to scars in chaotic systems the discussed quasi-modes in polygonal billiards become almost exact for high-excited states and for brevity they are designated as superscars. Many pictures of eigenfunctions for a triangular billiard and a barrier billiard which have clear superscar structures are presented in the paper. Special attention is given to the development of quantitative methods of detecting and analysing such superscars. In particular, it is demonstrated that the overlap between superscar waves associated with a fixed periodic orbit and eigenfunctions of a barrier billiard is distributed according to the Breit-Wigner distribution typical for weakly interacting quasi-modes (or doorway states). For special sub-class of rational polygonal billiards called Veech polygons where all periodic orbits can be calculated analytically it is argued and checked numerically that their eigenfunctions are fractal in the Fourier space.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Electroosmosis as a probe for electrostatic correlations – Archive ouverte HAL

### Ivan PalaiaIgor M. TellesAlexandre P. Dos SantosEmmanuel Trizac

^{1}#### Ivan Palaia, Igor M. Telles, Alexandre P. Dos Santos, Emmanuel Trizac. Electroosmosis as a probe for electrostatic correlations.

*Soft Matter*, Royal Society of Chemistry, 2021. ⟨hal-03223905⟩We study the role of ionic correlations on the electroosmotic flow in planar double-slit channels, without salt. We propose an analytical theory, based on recent advances in the understanding of correlated systems. We compare the theory with mean-field results and validate it by means of dissipative particle dynamics simulations. Interestingly, for some surface separations, correlated systems exhibit a larger flow than predicted by mean-field. We conclude that the electroosmotic properties of a charged system can be used, in general, to infer and weight the importance of electrostatic correlations therein.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Dynamical instantons and activated processes in mean-field glass models – Archive ouverte HAL

### Valentina Ros

^{1, 2}Giulio Biroli^{2}Chiara Cammarota#### Valentina Ros, Giulio Biroli, Chiara Cammarota. Dynamical instantons and activated processes in mean-field glass models.

*SciPost Physics*, SciPost Foundation, 2021, 10 (1), ⟨10.21468/SciPostPhys.10.1.002⟩. ⟨hal-03118004⟩We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Systèmes Désordonnés et Applications

## Counting statistics for noninteracting fermions in a d -dimensional potential – Archive ouverte HAL

### Naftali R. Smith

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Grégory Schehr^{3}#### Naftali R. Smith, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr. Counting statistics for noninteracting fermions in a d -dimensional potential.

*Physical Review E*, American Physical Society (APS), 2021, 103 (3), ⟨10.1103/PhysRevE.103.L030105⟩. ⟨hal-03179783⟩We develop a first-principle approach to compute the counting statistics in the ground-state of $N$ noninteracting spinless fermions in a general potential in arbitrary dimensions $d$ (central for $d>1$). In a confining potential, the Fermi gas is supported over a bounded domain. In $d=1$, for specific potentials, this system is related to standard random matrix ensembles. We study the quantum fluctuations of the number of fermions ${\cal N}_{\cal D}$ in a domain $\cal{D}$ of macroscopic size in the bulk of the support. We show that the variance of ${\cal N}_{\cal D}$ grows as $N^{(d-1)/d} (A_d \log N + B_d)$ for large $N$, and obtain the explicit dependence of $A_d, B_d$ on the potential and on the size of ${\cal D}$ (for a spherical domain in $d>1$). This generalizes the free-fermion results for microscopic domains, given in $d=1$ by the Dyson-Mehta asymptotics from random matrix theory. This leads us to conjecture similar asymptotics for the entanglement entropy of the subsystem $\cal{D}$, in any dimension, supported by exact results for $d=1$.

- 1. LPMS - Laboratoire de Physique des Matériaux et des Surfaces
- 2. Champs Aléatoires et Systèmes hors d'Équilibre
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Constrained non-crossing Brownian motions, fermions and the Ferrari–Spohn distribution – Archive ouverte HAL

### Tristan Gautié

^{1}Naftali R. Smith^{2, 1}#### Tristan Gautié, Naftali R. Smith. Constrained non-crossing Brownian motions, fermions and the Ferrari–Spohn distribution.

*J.Stat.Mech.*, 2021, 2103, pp.033212. ⟨10.1088/1742-5468/abe59c⟩. ⟨hal-03186169⟩A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work, we revisit the Ferrari–Spohn model of a Brownian bridge conditioned to avoid a moving wall, which pushes the system into a large-deviation regime. We extend this model to an arbitrary number N of non-crossing Brownian bridges. We obtain the joint distribution of the distances of the Brownian particles from the wall at an intermediate time in the form of the determinant of an N × N matrix whose entries are given in terms of the Airy function. We show that this distribution coincides with that of the positions of N spinless noninteracting fermions trapped by a linear potential with a hard wall. We then explore the N ≫ 1 behavior of the system. For simplicity we focus on the case where the wall’s position is given by a semicircle as a function of time, but we expect our results to be valid for any concave wall function.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Chaos-assisted long-range tunneling for quantum simulation – Archive ouverte HAL

### Maxime Martinez

^{1}Olivier Giraud^{2}Denis Ullmo^{2}Juliette Billy^{3}David Guéry-Odelin^{3}Bertrand Georgeot^{1}Gabriel Lemarié^{1, 4, 5}#### Maxime Martinez, Olivier Giraud, Denis Ullmo, Juliette Billy, David Guéry-Odelin, et al.. Chaos-assisted long-range tunneling for quantum simulation.

*Physical Review Letters*, American Physical Society, 2021, 126, pp.174102. ⟨10.1103/PhysRevLett.126.174102⟩. ⟨hal-02987847⟩We present an extension of the chaos-tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings tn ∝ 1/n between sites at a distance n. We provide numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law. Such systems can thus be used to enlarge the scope of quantum simulations in order to experimentally realize long-range models of condensed matter.

- 1. LPT - Laboratoire de Physique Théorique
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LCAR - Laboratoire Collisions Agrégats Réactivité
- 4. UMI 3654 - MajuLab
- 5. CQT - Centre for Quantum Technologies [Singapore]

## Casimir-Polder shift of ground-state hyperfine Zeeman sublevels of hydrogen isotopes in a micron-sized metallic cavity at finite temperature – Archive ouverte HAL

### Davide IacobacciGiuseppe BimonteThorsten Emig

^{1}#### Davide Iacobacci, Giuseppe Bimonte, Thorsten Emig. Casimir-Polder shift of ground-state hyperfine Zeeman sublevels of hydrogen isotopes in a micron-sized metallic cavity at finite temperature.

*Phys.Rev.A*, 2021, 103 (6), pp.062811. ⟨10.1103/PhysRevA.103.062811⟩. ⟨hal-03268883⟩The frequencies of transitions between hyperfine levels of ground-state atoms can be measured with exquisite precision using magnetic-resonance techniques. This makes hyperfine transitions ideal probes of QED effects originating from the interaction of atoms with the quantized electromagnetic field. One of the most remarkable effects predicted by QED is the Casimir-Polder shift experienced by the energy levels of atoms placed near one or more dielectric objects. Here we compute the Casimir-Polder shift and the width of hyperfine transitions between ground-state Zeeman sublevels of a hydrogen atom placed in a micron-sized metallic cavity, over a range of temperatures extending from cryogenic temperatures to room temperature. Results are presented also for deuterium and tritium. We predict shifts of the hyperfine transitions frequencies of a few tens of Hz that might be measurable with present-day magnetic resonance apparatus.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Bath-Induced Zeno Localization in Driven Many-Body Quantum Systems – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Denis M. Basko^{2}Markus Holzmann^{2}Alberto Rosso^{1}#### Thibaud Maimbourg, Denis M. Basko, Markus Holzmann, Alberto Rosso. Bath-Induced Zeno Localization in Driven Many-Body Quantum Systems.

*Phys.Rev.Lett.*, 2021, 126 (12), pp.120603. ⟨10.1103/PhysRevLett.126.120603⟩. ⟨hal-03186174⟩We study a quantum interacting spin system subject to an external drive and coupled to a thermal bath of vibrational modes, uncorrelated for different spins, serving as a model for dynamic nuclear polarization protocols. We show that even when the many-body eigenstates of the system are ergodic, a sufficiently strong coupling to the bath may effectively localize the spins due to many-body quantum Zeno effect. Our results provide an explanation of the breakdown of the thermal mixing regime experimentally observed above 4–5 K in these protocols.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPM2C - Laboratoire de physique et modélisation des milieux condensés

## Density scaling of generalized Lennard-Jones fluids in different dimensions – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Jeppe C. DyreLorenzo CostigliolaJeppe Dyre#### Thibaud Maimbourg, Jeppe C. Dyre, Lorenzo Costigliola, Jeppe Dyre. Density scaling of generalized Lennard-Jones fluids in different dimensions.

*SciPost Physics*, SciPost Foundation, 2020, 9 (6), ⟨10.21468/SciPostPhys.9.6.090⟩. ⟨hal-03117941⟩Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. This scaling property does not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, a comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Chiral active hexatics: Giant number fluctuations, waves and destruction of order – Archive ouverte HAL

### Ananyo Maitra

^{1}Martin Lenz^{2, 3}Raphael Voituriez^{1}#### Ananyo Maitra, Martin Lenz, Raphael Voituriez. Chiral active hexatics: Giant number fluctuations, waves and destruction of order.

*Physical Review Letters*, American Physical Society, 2020. ⟨hal-03085233⟩Active materials, composed of internally driven particles, have been shown to have properties that are qualitatively distinct matter at thermal equilibrium. However, most spectacular departures from equilibrium phase behaviour were thought to be confined to systems with polar or nematic asymmetry. In this paper we show that such departures are also displayed in more symmetric phases such as hexatics if in addition the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density, have giant number fluctuations. If the rotation-rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large lengthscale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them non-mutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

## Universal survival probability for a correlated random walk and applications to records – Archive ouverte HAL

### Bertrand Lacroix-A-Chez-Toine

^{1}Francesco Mori^{2}#### Bertrand Lacroix-A-Chez-Toine, Francesco Mori. Universal survival probability for a correlated random walk and applications to records.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020. ⟨hal-03085067⟩We consider a model of space-continuous one-dimensional random walk with simple correlation between the steps: the probability that two consecutive steps have same sign is $q$ with $0\leq q\leq 1$. The parameter $q$ allows thus to control the persistence of the random walk. We compute analytically the survival probability of a walk of $n$ steps, showing that it is independent of the jump distribution for any finite $n$. This universality is a consequence of the Sparre-Andersen theorem for random walks with uncorrelated and symmetric steps. We then apply this result to derive the distribution of the step at which the random walk reaches its maximum and the record statistics of the walk, which show the same universality. In particular, we show that the distribution of the number of records for a walk of $n\gg 1$ steps is the same as for a random walk with $n_{\rm eff}(q)=n/(2(1-q))$ uncorrelated and symmetrically distributed steps. We also show that in the regime where $n\to \infty$ and $q\to 1$ with $y=n(1-q)$, this model converges to the run-and-tumble particle, a persistent random walk often used to model the motion of bacteria. Our theoretical results are confirmed by numerical simulations.

- 1. Weizmann Institute of Science [Rehovot, Israël]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Efficient generation of random derangements with the expected distribution of cycle lengths – Archive ouverte HAL

### J. Ricardo G. Mendonça

^{1, 2}#### J. Ricardo G. Mendonça. Efficient generation of random derangements with the expected distribution of cycle lengths.

*Computational and Applied Mathematics*, Springer Verlag, 2020, 39 (3), ⟨10.1007/s40314-020-01295-4⟩. ⟨hal-03085042⟩We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random fixed-point-free involutions only, a.k.a. random perfect matchings on the complete graph. Our data indicate that the algorithms generate random samples with the expected distribution of cycle lengths, which we derive, and for relatively small samples, which can actually be very large in absolute numbers, we argue that they generate samples indistinguishable from the uniform distribution. Both algorithms are simple to understand and implement and possess a performance comparable to or better than those of currently known methods. Simulations suggest that the mixing time of the algorithm based on random restricted transpositions (in the total variance distance with respect to the distribution of cycle lengths) is $O(n^{a}\log{n}^{2})$ with $a \simeq \frac{1}{2}$ and $n$ the length of the derangement. We prove that the sequential importance sampling algorithm generates random derangements in $O(n)$ time with probability $O(1/n)$ of failing.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. USP - Universidade de São Paulo

## Strong-coupling theory of counterions with hard cores between symmetrically charged walls – Archive ouverte HAL

### Ladislav Šamaj

^{1}Martin Trulsson^{2}Emmanuel Trizac^{3}#### Ladislav Šamaj, Martin Trulsson, Emmanuel Trizac. Strong-coupling theory of counterions with hard cores between symmetrically charged walls.

*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.042604⟩. ⟨hal-03085023⟩By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on point-like counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two sub-populations, one for each plate, and integrates out one sub-population to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard sphere overlap are unavoidable, and thus rule out configurations.

- 1. SAS - Slovak Academy of Sciences
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Density scaling of generalized Lennard-Jones fluids in different dimensions – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Jeppe C. DyreLorenzo CostigliolaJeppe Dyre#### Thibaud Maimbourg, Jeppe C. Dyre, Lorenzo Costigliola, Jeppe Dyre. Density scaling of generalized Lennard-Jones fluids in different dimensions.

*SciPost Physics*, SciPost Foundation, 2020, 9 (6), ⟨10.21468/SciPostPhys.9.6.090⟩. ⟨hal-03117941⟩Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. This scaling property does not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, a comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Chiral active hexatics: Giant number fluctuations, waves and destruction of order – Archive ouverte HAL

### Ananyo Maitra

^{1}Martin Lenz^{2, 3}Raphael Voituriez^{1}#### Ananyo Maitra, Martin Lenz, Raphael Voituriez. Chiral active hexatics: Giant number fluctuations, waves and destruction of order.

*Physical Review Letters*, American Physical Society, 2020. ⟨hal-03085233⟩Active materials, composed of internally driven particles, have been shown to have properties that are qualitatively distinct matter at thermal equilibrium. However, most spectacular departures from equilibrium phase behaviour were thought to be confined to systems with polar or nematic asymmetry. In this paper we show that such departures are also displayed in more symmetric phases such as hexatics if in addition the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density, have giant number fluctuations. If the rotation-rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large lengthscale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them non-mutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

## Universal survival probability for a correlated random walk and applications to records – Archive ouverte HAL

### Bertrand Lacroix-A-Chez-Toine

^{1}Francesco Mori^{2}#### Bertrand Lacroix-A-Chez-Toine, Francesco Mori. Universal survival probability for a correlated random walk and applications to records.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020. ⟨hal-03085067⟩We consider a model of space-continuous one-dimensional random walk with simple correlation between the steps: the probability that two consecutive steps have same sign is $q$ with $0\leq q\leq 1$. The parameter $q$ allows thus to control the persistence of the random walk. We compute analytically the survival probability of a walk of $n$ steps, showing that it is independent of the jump distribution for any finite $n$. This universality is a consequence of the Sparre-Andersen theorem for random walks with uncorrelated and symmetric steps. We then apply this result to derive the distribution of the step at which the random walk reaches its maximum and the record statistics of the walk, which show the same universality. In particular, we show that the distribution of the number of records for a walk of $n\gg 1$ steps is the same as for a random walk with $n_{\rm eff}(q)=n/(2(1-q))$ uncorrelated and symmetrically distributed steps. We also show that in the regime where $n\to \infty$ and $q\to 1$ with $y=n(1-q)$, this model converges to the run-and-tumble particle, a persistent random walk often used to model the motion of bacteria. Our theoretical results are confirmed by numerical simulations.

- 1. Weizmann Institute of Science [Rehovot, Israël]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Efficient generation of random derangements with the expected distribution of cycle lengths – Archive ouverte HAL

### J. Ricardo G. Mendonça

^{1, 2}#### J. Ricardo G. Mendonça. Efficient generation of random derangements with the expected distribution of cycle lengths.

*Computational and Applied Mathematics*, Springer Verlag, 2020, 39 (3), ⟨10.1007/s40314-020-01295-4⟩. ⟨hal-03085042⟩We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random fixed-point-free involutions only, a.k.a. random perfect matchings on the complete graph. Our data indicate that the algorithms generate random samples with the expected distribution of cycle lengths, which we derive, and for relatively small samples, which can actually be very large in absolute numbers, we argue that they generate samples indistinguishable from the uniform distribution. Both algorithms are simple to understand and implement and possess a performance comparable to or better than those of currently known methods. Simulations suggest that the mixing time of the algorithm based on random restricted transpositions (in the total variance distance with respect to the distribution of cycle lengths) is $O(n^{a}\log{n}^{2})$ with $a \simeq \frac{1}{2}$ and $n$ the length of the derangement. We prove that the sequential importance sampling algorithm generates random derangements in $O(n)$ time with probability $O(1/n)$ of failing.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. USP - Universidade de São Paulo

## Strong-coupling theory of counterions with hard cores between symmetrically charged walls – Archive ouverte HAL

### Ladislav Šamaj

^{1}Martin Trulsson^{2}Emmanuel Trizac^{3}#### Ladislav Šamaj, Martin Trulsson, Emmanuel Trizac. Strong-coupling theory of counterions with hard cores between symmetrically charged walls.

*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.042604⟩. ⟨hal-03085023⟩By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on point-like counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two sub-populations, one for each plate, and integrates out one sub-population to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard sphere overlap are unavoidable, and thus rule out configurations.

- 1. SAS - Slovak Academy of Sciences
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Human running performance from real-world big data – Archive ouverte HAL

### Thorsten Emig

^{1}Jussi Peltonen#### Thorsten Emig, Jussi Peltonen. Human running performance from real-world big data.

*Nature Communications*, Nature Publishing Group, 2020, 11 (1), ⟨10.1038/s41467-020-18737-6⟩. ⟨hal-03065483⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Density scaling of generalized Lennard-Jones fluids in different dimensions – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Jeppe C. DyreLorenzo CostigliolaJeppe Dyre#### Thibaud Maimbourg, Jeppe C. Dyre, Lorenzo Costigliola, Jeppe Dyre. Density scaling of generalized Lennard-Jones fluids in different dimensions.

*SciPost Physics*, SciPost Foundation, 2020, 9 (6), ⟨10.21468/SciPostPhys.9.6.090⟩. ⟨hal-03117941⟩Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. This scaling property does not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, a comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Chiral active hexatics: Giant number fluctuations, waves and destruction of order – Archive ouverte HAL

### Ananyo Maitra

^{1}Martin Lenz^{2, 3}Raphael Voituriez^{1}#### Ananyo Maitra, Martin Lenz, Raphael Voituriez. Chiral active hexatics: Giant number fluctuations, waves and destruction of order.

*Physical Review Letters*, American Physical Society, 2020. ⟨hal-03085233⟩Active materials, composed of internally driven particles, have been shown to have properties that are qualitatively distinct matter at thermal equilibrium. However, most spectacular departures from equilibrium phase behaviour were thought to be confined to systems with polar or nematic asymmetry. In this paper we show that such departures are also displayed in more symmetric phases such as hexatics if in addition the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density, have giant number fluctuations. If the rotation-rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large lengthscale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them non-mutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

## Universal survival probability for a correlated random walk and applications to records – Archive ouverte HAL

### Bertrand Lacroix-A-Chez-Toine

^{1}Francesco Mori^{2}#### Bertrand Lacroix-A-Chez-Toine, Francesco Mori. Universal survival probability for a correlated random walk and applications to records.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020. ⟨hal-03085067⟩We consider a model of space-continuous one-dimensional random walk with simple correlation between the steps: the probability that two consecutive steps have same sign is $q$ with $0\leq q\leq 1$. The parameter $q$ allows thus to control the persistence of the random walk. We compute analytically the survival probability of a walk of $n$ steps, showing that it is independent of the jump distribution for any finite $n$. This universality is a consequence of the Sparre-Andersen theorem for random walks with uncorrelated and symmetric steps. We then apply this result to derive the distribution of the step at which the random walk reaches its maximum and the record statistics of the walk, which show the same universality. In particular, we show that the distribution of the number of records for a walk of $n\gg 1$ steps is the same as for a random walk with $n_{\rm eff}(q)=n/(2(1-q))$ uncorrelated and symmetrically distributed steps. We also show that in the regime where $n\to \infty$ and $q\to 1$ with $y=n(1-q)$, this model converges to the run-and-tumble particle, a persistent random walk often used to model the motion of bacteria. Our theoretical results are confirmed by numerical simulations.

- 1. Weizmann Institute of Science [Rehovot, Israël]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Efficient generation of random derangements with the expected distribution of cycle lengths – Archive ouverte HAL

### J. Ricardo G. Mendonça

^{1, 2}#### J. Ricardo G. Mendonça. Efficient generation of random derangements with the expected distribution of cycle lengths.

*Computational and Applied Mathematics*, Springer Verlag, 2020, 39 (3), ⟨10.1007/s40314-020-01295-4⟩. ⟨hal-03085042⟩We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random fixed-point-free involutions only, a.k.a. random perfect matchings on the complete graph. Our data indicate that the algorithms generate random samples with the expected distribution of cycle lengths, which we derive, and for relatively small samples, which can actually be very large in absolute numbers, we argue that they generate samples indistinguishable from the uniform distribution. Both algorithms are simple to understand and implement and possess a performance comparable to or better than those of currently known methods. Simulations suggest that the mixing time of the algorithm based on random restricted transpositions (in the total variance distance with respect to the distribution of cycle lengths) is $O(n^{a}\log{n}^{2})$ with $a \simeq \frac{1}{2}$ and $n$ the length of the derangement. We prove that the sequential importance sampling algorithm generates random derangements in $O(n)$ time with probability $O(1/n)$ of failing.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. USP - Universidade de São Paulo

## Strong-coupling theory of counterions with hard cores between symmetrically charged walls – Archive ouverte HAL

### Ladislav Šamaj

^{1}Martin Trulsson^{2}Emmanuel Trizac^{3}#### Ladislav Šamaj, Martin Trulsson, Emmanuel Trizac. Strong-coupling theory of counterions with hard cores between symmetrically charged walls.

*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.042604⟩. ⟨hal-03085023⟩By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on point-like counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two sub-populations, one for each plate, and integrates out one sub-population to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard sphere overlap are unavoidable, and thus rule out configurations.

- 1. SAS - Slovak Academy of Sciences
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Density scaling of generalized Lennard-Jones fluids in different dimensions – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Jeppe C. DyreLorenzo CostigliolaJeppe Dyre*SciPost Physics*, SciPost Foundation, 2020, 9 (6), ⟨10.21468/SciPostPhys.9.6.090⟩. ⟨hal-03117941⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

### Ananyo Maitra

^{1}Martin Lenz^{2, 3}Raphael Voituriez^{1}*Physical Review Letters*, American Physical Society, 2020. ⟨hal-03085233⟩- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

### Bertrand Lacroix-A-Chez-Toine

^{1}Francesco Mori^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020. ⟨hal-03085067⟩- 1. Weizmann Institute of Science [Rehovot, Israël]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

### J. Ricardo G. Mendonça

^{1, 2}*Computational and Applied Mathematics*, Springer Verlag, 2020, 39 (3), ⟨10.1007/s40314-020-01295-4⟩. ⟨hal-03085042⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. USP - Universidade de São Paulo

### Ladislav Šamaj

^{1}Martin Trulsson^{2}Emmanuel Trizac^{3}*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.042604⟩. ⟨hal-03085023⟩- 1. SAS - Slovak Academy of Sciences
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Density scaling of generalized Lennard-Jones fluids in different dimensions – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Jeppe C. DyreLorenzo CostigliolaJeppe Dyre*SciPost Physics*, SciPost Foundation, 2020, 9 (6), ⟨10.21468/SciPostPhys.9.6.090⟩. ⟨hal-03117941⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Density scaling of generalized Lennard-Jones fluids in different dimensions – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Jeppe C. DyreLorenzo CostigliolaJeppe Dyre*SciPost Physics*, SciPost Foundation, 2020, 9 (6), ⟨10.21468/SciPostPhys.9.6.090⟩. ⟨hal-03117941⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

### Ananyo Maitra

^{1}Martin Lenz^{2, 3}Raphael Voituriez^{1}*Physical Review Letters*, American Physical Society, 2020. ⟨hal-03085233⟩- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

### Bertrand Lacroix-A-Chez-Toine

^{1}Francesco Mori^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020. ⟨hal-03085067⟩- 1. Weizmann Institute of Science [Rehovot, Israël]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

### Ananyo Maitra

^{1}Martin Lenz^{2, 3}Raphael Voituriez^{1}*Physical Review Letters*, American Physical Society, 2020. ⟨hal-03085233⟩- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

### J. Ricardo G. Mendonça

^{1, 2}*Computational and Applied Mathematics*, Springer Verlag, 2020, 39 (3), ⟨10.1007/s40314-020-01295-4⟩. ⟨hal-03085042⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. USP - Universidade de São Paulo

### Bertrand Lacroix-A-Chez-Toine

^{1}Francesco Mori^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020. ⟨hal-03085067⟩- 1. Weizmann Institute of Science [Rehovot, Israël]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

### Ladislav Šamaj

^{1}Martin Trulsson^{2}Emmanuel Trizac^{3}*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.042604⟩. ⟨hal-03085023⟩- 1. SAS - Slovak Academy of Sciences
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

### J. Ricardo G. Mendonça

^{1, 2}*Computational and Applied Mathematics*, Springer Verlag, 2020, 39 (3), ⟨10.1007/s40314-020-01295-4⟩. ⟨hal-03085042⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. USP - Universidade de São Paulo

### Ladislav Šamaj

^{1}Martin Trulsson^{2}Emmanuel Trizac^{3}*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.042604⟩. ⟨hal-03085023⟩- 1. SAS - Slovak Academy of Sciences
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Human running performance from real-world big data – Archive ouverte HAL

### Thorsten Emig

^{1}Jussi Peltonen#### Thorsten Emig, Jussi Peltonen. Human running performance from real-world big data.

*Nature Communications*, Nature Publishing Group, 2020, 11 (1), ⟨10.1038/s41467-020-18737-6⟩. ⟨hal-03065483⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Wigner–Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity – Archive ouverte HAL

### Aurélien GrabschChristophe Texier

^{1}#### Aurélien Grabsch, Christophe Texier. Wigner–Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020, 53 (42), pp.425003. ⟨10.1088/1751-8121/aba215⟩. ⟨hal-03017007⟩We consider a multichannel wire with a disordered region of length $L$ and a reflecting boundary. The reflection of a wave of frequency $\omega$ is described by the scattering matrix $\mathcal{S}(\omega)$, encoding the probability amplitudes to be scattered from one channel to another. The Wigner-Smith time delay matrix $\mathcal{Q}=-\mathrm{i}\, \mathcal{S}^\dagger\partial_\omega\mathcal{S}$ is another important matrix encoding temporal aspects of the scattering process. In order to study its statistical properties, we split the scattering matrix in terms of two unitary matrices, $\mathcal{S}=\mathrm{e}^{2\mathrm{i}kL}\mathcal{U}_L\mathcal{U}_R$ (with $\mathcal{U}_L=\mathcal{U}_R^\mathrm{T}$ in the presence of TRS), and introduce a novel symmetrisation procedure for the Wigner-Smith matrix: $\widetilde{\mathcal{Q}} =\mathcal{U}_R\,\mathcal{Q}\,\mathcal{U}_R^\dagger = (2L/v)\,\mathbf{1}_N -\mathrm{i}\,\mathcal{U}_L^\dagger\partial_\omega\big(\mathcal{U}_L\mathcal{U}_R\big)\,\mathcal{U}_R^\dagger$, where $k$ is the wave vector and $v$ the group velocity. We demonstrate that $\widetilde{\mathcal{Q}}$ can be expressed under the form of an exponential functional of a matrix Brownian motion. For semi-infinite wires, $L\to\infty$, using a matricial extension of the Dufresne identity, we recover straightforwardly the joint distribution for $\mathcal{Q}$'s eigenvalues of Brouwer and Beenakker [Physica E 9 (2001) p. 463]. For finite length $L$, the exponential functional representation is used to calculate the first moments $\langle\mathrm{tr}(\mathcal{Q})\rangle$, $\langle\mathrm{tr}(\mathcal{Q}^2)\rangle$ and $\langle\big[\mathrm{tr}(\mathcal{Q})\big]^2\rangle$. Finally we derive a partial differential equation for the resolvent $g(z;L)=\lim_{N\to\infty}(1/N)\,\mathrm{tr}\big\{\big( z\,\mathbf{1}_N - N\,\mathcal{Q}\big)^{-1}\big\}$ in the large $N$ limit.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Velocity and diffusion constant of an active particle in a one-dimensional force field – Archive ouverte HAL

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}Gregory Schehr^{2}#### Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Velocity and diffusion constant of an active particle in a one-dimensional force field.

*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020, 130 (4), pp.40002. ⟨10.1209/0295-5075/130/40002⟩. ⟨hal-02881224⟩We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of period $L$. They involve the "active potential" which allows to define a global bias. Upon varying parameters, such as an external force $F$, the dynamics undergoes transitions from non-ergodic trapped states, to various moving states, some with non analyticities in the $V_L$ versus $F$ curve. A random landscape in the presence of a bias leads, for large $L$, to anomalous diffusion $x \sim t^\mu$, $\mu<1$, or to a phase with a finite velocity that we calculate.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle – Archive ouverte HAL

### Francesco Mori

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle.

*Physical Review Letters*, American Physical Society, 2020, 124 (9), ⟨10.1103/PhysRevLett.124.090603⟩. ⟨hal-02512214⟩We consider an active run-and-tumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$-component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Champs Aléatoires et Systèmes hors d'Équilibre

### Bertrand Lacroix-A-Chez-Toine

^{1}Francesco Mori^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020. ⟨hal-03085067⟩- 1. Weizmann Institute of Science [Rehovot, Israël]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Universal Scaling of the Velocity Field in Crack Front Propagation – Archive ouverte HAL

### Clément Le Priol

^{1}Pierre Le Doussal^{2}Laurent Ponson^{3}Alberto Rosso^{4}Julien Chopin^{5}#### Clément Le Priol, Pierre Le Doussal, Laurent Ponson, Alberto Rosso, Julien Chopin. Universal Scaling of the Velocity Field in Crack Front Propagation.

*Physical Review Letters*, American Physical Society, 2020, 124 (6), ⟨10.1103/PhysRevLett.124.065501⟩. ⟨hal-02512228⟩The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.

- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. Champs Aléatoires et Systèmes hors d'Équilibre
- 3. DALEMBERT - Institut Jean Le Rond d'Alembert
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. IF-UFB - Instituto de Fisica, Universidade Federal da Bahia

## Universal properties of a run-and-tumble particle in arbitrary dimension – Archive ouverte HAL

### Francesco Mori

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Grégory Schehr^{1}#### Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr. Universal properties of a run-and-tumble particle in arbitrary dimension.

*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.042133⟩. ⟨hal-03010271⟩We consider an active run-and-tumble particle (RTP) in $d$ dimensions, starting from the origin and evolving over a time interval $[0,t]$. We examine three different models for the dynamics of the RTP: the standard RTP model with instantaneous tumblings, a variant with instantaneous runs and a general model in which both the tumblings and the runs are non-instantaneous. For each of these models, we use the Sparre Andersen theorem for discrete-time random walks to compute exactly the probability that the $x$ component does not change sign up to time $t$, showing that it does not depend on $d$. As a consequence of this result, we compute exactly other $x$-component properties, namely the distribution of the time of the maximum and the record statistics, showing that they are universal, i.e. they do not depend on $d$. Moreover, we show that these universal results hold also if the speed $v$ of the particle after each tumbling is random, drawn from a generic probability distribution. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 124, 090603 (2020)].

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris

## Universal gap statistics for random walks for a class of jump densities – Archive ouverte HAL

### Matteo Battilana

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}#### Matteo Battilana, Satya N. Majumdar, Gregory Schehr. Universal gap statistics for random walks for a class of jump densities.

*Markov Processes And Related Fields*, Polymat Publishing Company, 2020. ⟨hal-02518812⟩We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim |\eta|^p \,e^{-|\eta|}$, parametrized by a non-negative integer $p$. Our main focus is on the statistics of the gaps $d_{k,n}$ between two successive maxima $d_{k,n}=M_{k,n}-M_{k+1,n}$ where $M_{k,n}$ is the $k$-th maximum of the RW between step 1 and step $n$. In the limit of large $n$, we show that the probability density function of the gaps $P_{k,n}(\Delta) = \Pr(d_{k,n} = \Delta)$ reaches a stationary density $P_{k,n}(\Delta) \to p_k(\Delta)$. For large $k$, we demonstrate that the typical fluctuations of the gap, for $d_{k,n}= O(1/\sqrt{k})$ (and $n \to \infty$), are described by a non-trivial scaling function that is independent of $k$ and of the jump probability density function $f_p(\eta)$, thus corroborating our conjecture about the universality of the regime of typical fluctuations (see G. Schehr, S. N. Majumdar, Phys. Rev. Lett. 108, 040601 (2012)). We also investigate the large fluctuations of the gap, for $d_{k,n} = O(1)$ (and $n \to \infty$), and show that these two regimes of typical and large fluctuations of the gaps match smoothly.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Truncated moment sequences and a solution to the channel separability problem – Archive ouverte HAL

### Nadia Milazzo

^{1}Daniel BraunOlivier Giraud^{1}#### Nadia Milazzo, Daniel Braun, Olivier Giraud. Truncated moment sequences and a solution to the channel separability problem.

*Physical Review A*, American Physical Society 2020, 102 (5), ⟨10.1103/PhysRevA.102.052406⟩. ⟨hal-03017063⟩We consider the problem of separability of quantum channels via the Choi matrix representation given by the Choi-Jamio{\l}kowski isomorphism. We explore three classes of separability across different cuts between systems and ancillae and we provide a solution based on the mapping of the coordinates of the Choi state (in a fixed basis) to a truncated moment sequence (tms) $y$. This results in an algorithm which gives a separability certificate using semidefinite programming. The computational complexity and the performance of it depend on the number of variables $n$ in the tms and on the size of the moment matrix $M_t(y)$ of order $t$. We exploit the algorithm to numerically investigate separability of families of 2-qubit and single-qutrit channels; in the latter case we can provide an answer for examples explored earlier through the criterion based on the negativity $N$, a criterion which remains inconclusive for Choi matrices with $N=0$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Toward the full short-time statistics of an active Brownian particle on the plane – Archive ouverte HAL

### Satya N. Majumdar

^{1}Baruch Meerson#### Satya N. Majumdar, Baruch Meerson. Toward the full short-time statistics of an active Brownian particle on the plane.

*Physical Review E*, American Physical Society (APS), 2020, 102 (2), ⟨10.1103/PhysRevE.102.022113⟩. ⟨hal-03017046⟩We study the position distribution of a single active Brownian particle (ABP) on the plane. We show that this distribution has a compact support, the boundary of which is an expanding circle. We focus on a short-time regime and employ the optimal fluctuation method (OFM) to study large deviations of the particle position coordinates $x$ and $y$. We determine the optimal paths of the ABP, conditioned on reaching specified values of $x$ and $y$, and the large deviation functions of the marginal distributions of $x$, and of $y$. These marginal distributions match continuously with "near tails" of the $x$ and $y$ distributions of typical fluctuations, studied earlier. We also calculate the large deviation function of the joint $x$ and $y$ distribution $P(x,y,t)$ in a vicinity of a special "zero-noise" point, and show that $\ln P(x,y,t)$ has a nontrivial self-similar structure as a function of $x$, $y$ and $t$. The joint distribution vanishes extremely fast at the expanding circle, exhibiting an essential singularity there. This singularity is inherited by the marginal $x$- and $y$-distributions. We argue that this fingerprint of the short-time dynamics remains there at all times.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Topological effects and conformal invariance in long-range correlated random surfaces – Archive ouverte HAL

### Nina Javerzat

^{1}Sebastian Grijalva^{1}Alberto Rosso^{1}Raoul Santachiara^{1}#### Nina Javerzat, Sebastian Grijalva, Alberto Rosso, Raoul Santachiara. Topological effects and conformal invariance in long-range correlated random surfaces.

*SciPost Phys.*, 2020, 9 (4), pp.050. ⟨10.21468/SciPostPhys.9.4.050⟩. ⟨hal-02863162⟩We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter ($H$) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $H\leq-\frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For $-\frac{3}{4}

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence – Archive ouverte HAL

### Giuseppe Petrillo

^{1}Eugenio Lippiello^{1}François Landes^{2, 3}Alberto Rosso^{4}#### Giuseppe Petrillo, Eugenio Lippiello, François Landes, Alberto Rosso. The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence.

*Nature Communications*, Nature Publishing Group, 2020, 11 (1), ⟨10.1038/s41467-020-16811-7⟩. ⟨hal-02942365⟩Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of after-shocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.

- 1. Università degli studi della Campania "Luigi Vanvitelli"
- 2. UP11 UFR Sciences - Université Paris-Sud - Paris 11 - Faculté des Sciences
- 3. TAU - TAckling the Underspecified
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The convex hull of the run-and-tumble particle in a plane – Archive ouverte HAL

### Alexander K HartmannSatya N Majumdar

^{1}Hendrik Schawe^{2}Gregory Schehr^{1}Alexander Hartmann^{2}Satya Majumdar^{1}#### Alexander K Hartmann, Satya N Majumdar, Hendrik Schawe, Gregory Schehr, Alexander Hartmann, et al.. The convex hull of the run-and-tumble particle in a plane.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2020, 2020 (5), pp.053401. ⟨10.1088/1742-5468/ab7c5f⟩. ⟨hal-02881103⟩We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its direction randomly. We consider two different statistical ensembles where we either fix (i) the total number of tumblings $n$ or (ii) the total duration $t$ of the time interval. In both cases, we derive exact expressions for the average perimeter of the convex hull and then compare to numerical estimates finding excellent agreement. Further, we numerically compute the full distribution of the perimeter using Markov chain Monte Carlo techniques, in both ensembles, probing the far tails of the distribution, up to a precision smaller than $10^{-100}$. This also allows us to characterize the rare events that contribute to the tails of these distributions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Oldenburg

## Symmetries in $B \to D^* \ell \nu$ angular observables – Archive ouverte HAL

### Marcel AlgueróSébastien Descotes-Genon

^{1}Joaquim MatiasMartín Novoa-Brunet^{2}#### Marcel Algueró, Sébastien Descotes-Genon, Joaquim Matias, Martín Novoa-Brunet. Symmetries in $B \to D^* \ell \nu$ angular observables.

*JHEP*, 2020, 06, pp.156. ⟨10.1007/JHEP06(2020)156⟩. ⟨hal-02518081⟩We apply the formalism of amplitude symmetries to the angular distribution of the decays B → D$^{∗}$ℓν for ℓ = e, μ, τ . We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the D$^{∗}$ using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure $ {F}_L^{D\ast } $ in B → D$^{∗}$τν and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify three observables which may exhibit a tension if the experimental value of $ {F}_L^{D\ast } $ remains high. We discuss how these relations can be exploited for binned measurements. We also propose a new observable that could test for specific scenarios of New Physics generated by light right-handed neutrinos. Finally we study the prospects of testing these relations based on the projected experimental sensitivity of new experiments.

- 1. IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Superfluid transition in disordered dipolar Fermi gases – Archive ouverte HAL

### S. I. MatveenkoV. I. YudsonB. L. AltshulerG. V. Shlyapnikov

^{1}#### S. I. Matveenko, V. I. Yudson, B. L. Altshuler, G. V. Shlyapnikov. Superfluid transition in disordered dipolar Fermi gases.

*Physical Review A*, American Physical Society 2020. ⟨hal-03017056⟩We consider a weakly interacting two-component Fermi gas of dipolar particles (magnetic atoms or polar molecules) in the two-dimensional geometry. The dipole-dipole interaction (together with the short-range interaction at Feshbach resonances) for dipoles perpendicular to the plane of translational motion may provide a superfluid transition. The dipole-dipole scattering amplitude is momentum dependent, which violates the Anderson theorem claiming the independence of the transition temperature on the presence of weak disorder. We have shown that the disorder can strongly increase the critical temperature (up to 10 nK at realistic densities). This opens wide possibilities for the studies of the superfluid regime in weakly interacting Fermi gases, which was not observed so far.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

### Ladislav Šamaj

^{1}Martin Trulsson^{2}Emmanuel Trizac^{3}*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.042604⟩. ⟨hal-03085023⟩- 1. SAS - Slovak Academy of Sciences
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Stochastic Resetting and Applications – Archive ouverte HAL

### Martin Evans

^{1}Satya Majumdar^{2}Grégory Schehr^{2}#### Martin Evans, Satya Majumdar, Grégory Schehr. Stochastic Resetting and Applications.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020. ⟨hal-03010293⟩In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field. PACS numbers: 05.40.-a, 05.70.Fh, 02.50.Ey, 64.60.-i arXiv:1910.07993v2 [cond-mat.stat-mech]

- 1. Université d'Edimbourg
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Stochastic growth in time-dependent environments – Archive ouverte HAL

### Guillaume Barraquand

^{1}Pierre Le Doussal^{1}Alberto Rosso^{2}#### Guillaume Barraquand, Pierre Le Doussal, Alberto Rosso. Stochastic growth in time-dependent environments.

*Physical Review E*, American Physical Society (APS), 2020, 101 (4), ⟨10.1103/PhysRevE.101.040101⟩. ⟨hal-02565202⟩We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{-\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution saturates at large times towards a non-universal limiting distribution. When $\alpha<1/2$ the fluctuation field is governed by scaling exponents depending on $\alpha$ and the limiting statistics are similar to the case when $c(t)$ is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential (2) An exactly solvable discretization, the log-gamma polymer model (3) Numerical simulations.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Statistics of the number of records for random walks and Lévy flights on a 1D lattice – Archive ouverte HAL

### Philippe Mounaix

^{1}Satya Majumdar^{2}Grégory Schehr^{2}#### Philippe Mounaix, Satya Majumdar, Grégory Schehr. Statistics of the number of records for random walks and Lévy flights on a 1D lattice.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020, 53 (41), pp.415003. ⟨10.1088/1751-8121/abac97⟩. ⟨hal-02958283⟩We study the statistics of the number of records R n for a symmetric, n-step, discrete jump process on a 1D lattice. At a given step, the walker can jump by arbitrary lattice units drawn from a given symmetric probability distribution. This process includes, as a special case, the standard nearest neighbor lattice random walk. We derive explicitly the generating function of the distribution P (R n) of the number of records, valid for arbitrary discrete jump distributions. As a byproduct, we provide a relatively simple proof of the generalized Sparre Andersen theorem for the survival probability of a random walk on a line, with discrete or continuous jump distributions. For the discrete jump process, we then derive the asymptotic large n behavior of P (R n) as well as of the average number of records E(R n). We show that unlike the case of random walks with symmetric and continuous jump distributions where the record statistics is strongly universal (i.e., independent of the jump distribution for all n), the record statistics for lattice walks depends on the jump distribution for any fixed n. However, in the large n limit, we show that the distribution of the scaled record number R n /E(R n) approaches a universal, half-Gaussian form for any discrete jump process. The dependence on the jump distribution enters only through the scale factor E(R n), which we also compute in the large n limit for arbitrary jump distributions. We present explicit results for a few examples and provide numerical checks of our analytical predictions.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## State transition graph of the Preisach model and the role of return-point memory – Archive ouverte HAL

### M. Mert Terzi

^{1}Muhittin Mungan#### M. Mert Terzi, Muhittin Mungan. State transition graph of the Preisach model and the role of return-point memory.

*Physical Review E*, 2020, 102 (1), ⟨10.1103/PhysRevE.102.012122⟩. ⟨hal-02908545⟩The Preisach model has been useful as a null-model for understanding memory formation in periodically driven disordered systems. In amorphous solids for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by one of us, the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between soft-spots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying soft-spot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return point memory in organizing the graph into a hierarchy of loops and sub-loops. Our analysis reveals that the topology of a large portion of this graph is actually not governed by the values of the switching fields that describe the individual hysteretic behavior of the individual elements, but by a coarser parameter, a permutation $\rho$ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states $| \mathcal{R} |$ constituting the main hysteresis loop and its nested subloops. We find that $| \mathcal{R} |$ is equal to the number of increasing subsequences contained in the permutation $\rho$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Spectral statistics of random Toeplitz matrices – Archive ouverte HAL

### Eugene Bogomolny

^{1}#### Eugene Bogomolny. Spectral statistics of random Toeplitz matrices.

*Physical Review E*, American Physical Society (APS), 2020, 102 (4), ⟨10.1103/PhysRevE.102.040101⟩. ⟨hal-03017017⟩Spectral statistics of hermitian random Toeplitz matrices with independent identically distributed elements is investigated numerically. It is found that the eigenvalue statistics of complex Toeplitz matrices is surprisingly well approximated by the semi-Poisson distribution belonging to intermediate-type statistics observed in certain pseudo-integrable billiards. The origin of intermediate behaviour could be attributed to the fact that Fourier transformed random Toeplitz matrices have the same slow decay outside the main diagonal as critical random matrix ensembles. The statistical properties of the full spectrum of real random Toeplitz matrices with i.i.d. elements are close to the Poisson distribution but each of their constituted sub-spectra is again well described by the semi-Poisson distribution. The findings open new perspective in intermediate statistics.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Semiclassical evaluation of expectation values – Archive ouverte HAL

### Kush Mohan MittalOlivier Giraud

^{1}Denis Ullmo^{1}#### Kush Mohan Mittal, Olivier Giraud, Denis Ullmo. Semiclassical evaluation of expectation values.

*Physical Review E*, American Physical Society (APS), 2020. ⟨hal-03017036⟩Semiclassical Mechanics allows for a description of quantum systems which preserves their phase information, while using only the system's classical dynamics as an input. Over the time an identification has been developed between stationary phase approximation and semiclassical mechanics. Although it is true that in most of the cases in semiclassical mechanics the significant contributions come from the neighborhood of the stationary points, there are some important exceptions to it. In this paper we address one of these exceptions, occurring in the evaluation of the time evolution of the expectation value of an operator. We explain why it is necessary to include contributions which are not in the neighborhood of stationary points and provide new semiclassical expressions for the evolution of the expectation values. For our analysis we employ and discuss two major semiclassical tools. The first one is the association of the quantum evolution of a wavefunction to the classical evolution of a Lagrangian manifold, as done by Maslov. The second one is the derivation of an expression for the semiclassical Wigner function whose properties under canonical transformation are made explicit. Using the canonical invariance of the formalism, we derive an expression for the expectation value of observables for the one-dimensional case and then generalize it to higher dimensions. We find that the expression can be written as the sum of a classical contribution which corresponds to what is referred to as the Truncated Wigner Approximation (TWA) in the cold-atoms physics context, or the Linearized Semiclassical Initial Value Representation(LSC-IVR) in chemical or molecular physics, and additional terms associated with interferences. Along the way, we get a deeper understanding of the origin of these interference effects and an intuitive geometric picture associated with them.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Self-isolation or borders closing: What prevents the spread of the epidemic better? – Archive ouverte HAL

### O. ValbaV. AvetisovA. GorskyS. Nechaev

^{1}#### O. Valba, V. Avetisov, A. Gorsky, S. Nechaev. Self-isolation or borders closing: What prevents the spread of the epidemic better?.

*Physical Review E*, American Physical Society (APS), 2020, 102 (1), ⟨10.1103/PhysRevE.102.010401⟩. ⟨hal-03009765⟩Pandemic distribution of COVID-19 in the world has motivated us to discuss combined effects of network clustering and adaptivity on epidemic spreading. We address the question concerning the choice of optimal mechanism for most effective prohibiting disease propagation in a connected network: adaptive clustering, which mimics self-isolation (SI) in local communities, or sharp instant clustering, which looks like frontiers closing (FC) between cities and countries. SI-networks are "adaptively grown" under condition of maximization of small cliques in the entire network, while FC-networks are "instantly created". Running the standard SIR model on clustered SI- and FC-networks, we demonstrate that the adaptive network clustering prohibits the epidemic spreading better than the instant clustering in the network with similar parameters. We found that SI model has scale-free property for degree distribution $P(k)\sim k^{\eta}$ with small critical exponent $-2<\eta<-1$ and argue that scale-free behavior emerges due to the randomness in the initial degree distributions and is absent for random regular graphs.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Schrödinger approach to Mean Field Games with negative coordination – Archive ouverte HAL

### Thibault Bonnemain

^{1}Thierry Gobron^{2}Denis Ullmo^{1}#### Thibault Bonnemain, Thierry Gobron, Denis Ullmo. Schrödinger approach to Mean Field Games with negative coordination.

*SciPost Physics*, SciPost Foundation, 2020, ⟨10.21468/SciPostPhys.9.4.059⟩. ⟨hal-02923105⟩Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled agents in interaction. Here we consider such systems when the interactions between agents result in a negative coordination and analyze the behavior of the associated system of coupled PDEs using the now well established correspondence with the non linear Schr\"odinger equation. We focus on the long optimization time limit and on configurations such that the game we consider goes through different regimes in which the relative importance of disorder, interactions between agents and external potential varies, which makes possible to get insights on the role of the forward-backward structure of the Mean Field Game equations in relation with the way these various regimes are connected.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPP - Laboratoire Paul Painlevé - UMR 8524

## Scalable quantum computing with qudits on a graph – Archive ouverte HAL

### E. O. Kiktenko

^{1}A. S. NikolaevaPeng XuG. V. Shlyapnikov^{2}A. K. Fedorov^{3}#### E. O. Kiktenko, A. S. Nikolaeva, Peng Xu, G. V. Shlyapnikov, A. K. Fedorov. Scalable quantum computing with qudits on a graph.

*Physical Review A*, American Physical Society 2020, 101 (2), ⟨10.1103/PhysRevA.101.022304⟩. ⟨hal-02512218⟩We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multi-qudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.

- 1. IPE - Schmidt United Institute of Physics of the Earth [Moscow]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Russian Quantum Center

## Rigorous bounds on dynamical response functions and time-translation symmetry breaking – Archive ouverte HAL

### Marko Medenjak

^{1}Tomaz Prosen^{2}Lenart Zadnik^{3}#### Marko Medenjak, Tomaz Prosen, Lenart Zadnik. Rigorous bounds on dynamical response functions and time-translation symmetry breaking.

*SciPost Physics*, SciPost Foundation, 2020, 9 (1), ⟨10.21468/SciPostPhys.9.1.003⟩. ⟨hal-02935659⟩Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e., extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Flo-quet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.

- 1. IPM - institut de Physique Théorique Philippe Meyer
- 2. FMF - Faculty of Mathematics and Physics [Ljubljana]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Reversal of contractility as a signature of self-organization in cytoskeletal bundles – Archive ouverte HAL

### Martin Lenz

^{1}#### Martin Lenz. Reversal of contractility as a signature of self-organization in cytoskeletal bundles.

*eLife*, eLife Sciences Publication, 2020, 9, ⟨10.7554/eLife.51751⟩. ⟨hal-02518848⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p -Spin Model – Archive ouverte HAL

### Giampaolo Folena

^{1}Silvio Franz^{1}Federico Ricci-Tersenghi#### Giampaolo Folena, Silvio Franz, Federico Ricci-Tersenghi. Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p -Spin Model.

*Physical Review X*, American Physical Society, 2020, 10 (3), ⟨10.1103/PhysRevX.10.031045⟩. ⟨hal-03017024⟩The spherical p-spin model is not only a fundamental model in statistical mechanics of disordered system, but has recently gained popularity since many hard problems in machine learning can be mapped on it. Thus the study of the out of equilibrium dynamics in this model is interesting both for the glass physics and for its implications on algorithms solving NP-hard problems. We revisit the long-time limit of the out of equilibrium dynamics of mean-field spherical mixed p-spin models. We consider quenches (gradient descent dynamics) starting from initial conditions thermalized at some temperature in the ergodic phase. We perform numerical integration of the dynamical mean-field equations of the model and we find an unexpected dynamical phase transition. Below an onset temperature, higher than the dynamical transition temperature, the asymptotic energy goes below the "threshold energy" of the dominant marginal minima of the energy function and memory of the initial condition is kept. This behavior, not present in the pure spherical p-spin model, resembles closely the one observed in simulations of glass-forming liquids. We then investigate the nature of the asymptotic dynamics, finding an aging solution that relaxes towards deep marginal minima, evolving on a restricted marginal manifold. Careful analysis, however, rules out simple aging solutions. We compute the constrained complexity in the aim of connecting the asymptotic solution to the energy landscape.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Optimizing Brownian escape rates by potential shaping – Archive ouverte HAL

### Marie Chupeau

^{1}Jannes GladrowAlexei Chepelianskii^{2}Ulrich F. KeyserEmmanuel Trizac^{1}Ulrich Keyser#### Marie Chupeau, Jannes Gladrow, Alexei Chepelianskii, Ulrich F. Keyser, Emmanuel Trizac, et al.. Optimizing Brownian escape rates by potential shaping.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2020, 117 (3), pp.1383-1388. ⟨10.1073/pnas.1910677116⟩. ⟨hal-02512216⟩Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under two different regularizations, and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPCT - Laboratoire de Physico-Chimie Théorique

## Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States – Archive ouverte HAL

### John MartinStefan WeigertOlivier Giraud

^{1}#### John Martin, Stefan Weigert, Olivier Giraud. Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States.

*Quantum*, Verein, 2020. ⟨hal-02881098⟩Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids – Archive ouverte HAL

### Alessandro Manacorda

^{1}Gregory Schehr^{2}Francesco Zamponi^{1}#### Alessandro Manacorda, Gregory Schehr, Francesco Zamponi. Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids.

*Journal of Chemical Physics*, American Institute of Physics, 2020, 152 (16), pp.164506. ⟨10.1063/5.0007036⟩. ⟨hal-02554137⟩- 1. Systèmes Désordonnés et Applications
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Non-Hermitian quantum impurity systems in and out of equilibrium: Noninteracting case – Archive ouverte HAL

### Takato YoshimuraKemal Bidzhiev

^{1}Hubert Saleur#### Takato Yoshimura, Kemal Bidzhiev, Hubert Saleur. Non-Hermitian quantum impurity systems in and out of equilibrium: Noninteracting case.

*Physical Review B*, American Physical Society, 2020, 102 (12), ⟨10.1103/PhysRevB.102.125124⟩. ⟨hal-03017010⟩We provide systematic analysis on a non-Hermitian PT -symmetric quantum impurity system both in and out of equilibrium, based on exact computations. In order to understand the interplay between non-Hermiticity and Kondo physics, we focus on a prototypical noninteracting impurity system, the resonant level model, with complex coupling constants. Explicitly constructing biorthogonal basis, we study its thermodynamic properties as well as the Loschmidt echo starting from the initially disconnected two free fermion chains. Remarkably, we observe the universal crossover physics in the Loschmidt echo, both in the PT broken and unbroken regimes. We also find that the ground state quantities we compute in the PT broken regime can be obtained by analytic continuation. It turns out that Kondo screening ceases to exist in the PT broken regime, which was also previously predicted in the non-hermitian Kondo model. All the analytical results are corroborated against biorthogonal free fermion numerics.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Multi-component colloidal gels: interplay between structure and mechanical properties – Archive ouverte HAL

### Claudia Ferreiro-CordovaMehdi Bouzid

^{1}Emanuela del GadoGiuseppe Foffi^{2}Claudia Ferreiro-Córdova#### Claudia Ferreiro-Cordova, Mehdi Bouzid, Emanuela del Gado, Giuseppe Foffi, Claudia Ferreiro-Córdova. Multi-component colloidal gels: interplay between structure and mechanical properties.

*Soft Matter*, Royal Society of Chemistry, 2020, 16 (18), pp.4414-4421. ⟨10.1039/C9SM02410G⟩. ⟨hal-02881157⟩We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of component leads to softer solids that can accomodate progressively larger strain before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work {provides new insight into mechanisms at play for controlling the material properties and open the road to new design principles for} soft composite solids

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes – Archive ouverte HAL

### Guillaume Lamour

^{1}Antoine Allard^{1, 2}Juan Pelta^{1}Sid Labdi^{1}Martin Lenz^{3}Clément Campillo^{1}#### Guillaume Lamour, Antoine Allard, Juan Pelta, Sid Labdi, Martin Lenz, et al.. Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes.

*Physical Review X*, American Physical Society, 2020, 10 (1), pp.011031. ⟨10.1103/PhysRevX.10.011031⟩. ⟨hal-02512272⟩Membrane nanotubes are continuously assembled and disassembled by the cell to generate and dispatch transport vesicles, for instance, in endocytosis. While these processes crucially involve the ill-understood local mechanics of the nanotube, existing micromanipulation assays only give access to its global mechanical properties. Here we develop a new platform to study this local mechanics using atomic force microscopy (AFM). On a single coverslip we quickly generate millions of substrate-bound nanotubes, out of which dozens can be imaged by AFM in a single experiment. A full theoretical description of the AFM tip-membrane interaction allows us to accurately relate AFM measurements of the nanotube heights, widths, and rigidities to the membrane bending rigidity and tension, thus demonstrating our assay as an accurate probe of nanotube mechanics. We reveal a universal relationship between nanotube height and rigidity, which is unaffected by the specific conditions of attachment to the substrate. Moreover, we show that the parabolic shape of force-displacement curves results from thermal fluctuations of the membrane that collides intermittently with the AFM tip. We also show that membrane nanotubes can exhibit high resilience against extreme lateral compression. Finally, we mimic in vivo actin polymerization on nanotubes and use AFM to assess the induced changes in nanotube physical properties. Our assay may help unravel the local mechanics of membrane-protein interactions, including membrane remodeling in nanotube scission and vesicle formation.

- 1. LAMBE - UMR 8587 - Laboratoire Analyse, Modélisation et Matériaux pour la Biologie et l'Environnement
- 2. PCC - Physico-Chimie-Curie
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Lattice walk area combinatorics, some remarkable trigonometric sums and Apéry-like numbers – Archive ouverte HAL

### Stéphane Ouvry

^{1}Alexios Polychronakos#### Stéphane Ouvry, Alexios Polychronakos. Lattice walk area combinatorics, some remarkable trigonometric sums and Apéry-like numbers.

*Nucl.Phys.B*, 2020, 960, pp.115174. ⟨10.1016/j.nuclphysb.2020.115174⟩. ⟨hal-02886896⟩Explicit algebraic area enumeration formulae are derived for various lattice walks generalizing the canonical square lattice walks, and in particular for the triangular lattice chiral walks recently introduced by the authors. A key element in the enumeration is the derivation of some identities involving some remarkable trigonometric sums –which are also important building blocks of non trivial quantum models such as the Hofstadter model– and their explicit rewriting in terms of multiple binomial sums. An intriguing connection is also made with number theory and some classes of Apéry-like numbers, the cousins of the Apéry numbers which play a central role in irrationality considerations for ζ(2) and ζ(3) .

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Last-Passage Time for Linear Diffusions and Application to the Emptying Time of a Box – Archive ouverte HAL

### Alain Comtet

^{1}Françoise Cornu^{1}Grégory Schehr^{1}#### Alain Comtet, Françoise Cornu, Grégory Schehr. Last-Passage Time for Linear Diffusions and Application to the Emptying Time of a Box.

*Journal of Statistical Physics*, Springer Verlag, 2020, ⟨10.1007/s10955-020-02637-6⟩. ⟨hal-02988500⟩We study the statistics of last-passage time for linear diffusions. First we present an elementary derivation of the Laplace transform of the probability density of the last-passage time, thus recovering known results from the mathematical literature. We then illustrate them on several explicit examples. In a second step we study the spectral properties of the Schr\"{o}dinger operator associated to such diffusions in an even potential $U(x) = U(-x)$, unveiling the role played by the so-called Weyl coefficient. Indeed, in this case, our approach allows us to relate the last-passage times for dual diffusions (i.e., diffusions driven by opposite force fields) and to obtain new explicit formulae for the mean last-passage time. We further show that, for such even potentials, the small time $t$ expansion of the mean last-passage time on the interval $[0,t]$ involves the Korteveg-de Vries invariants, which are well known in the theory of Schr\"odinger operators. Finally, we apply these results to study the emptying time of a one-dimensional box, of size $L$, containing $N$ independent Brownian particles subjected to a constant drift. In the scaling limit where both $N \to \infty$ and $L \to \infty$, keeping the density $\rho = N/L$ fixed, we show that the limiting density of the emptying time is given by a Gumbel distribution. Our analysis provides a new example of the applications of extreme value statistics to out-of-equilibrium systems.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Large deviations of glassy effective potentials – Archive ouverte HAL

### Silvio Franz

^{1}Jacopo Rocchi^{1}#### Silvio Franz, Jacopo Rocchi. Large deviations of glassy effective potentials.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020, 53 (48), pp.485002. ⟨10.1088/1751-8121/ab9aeb⟩. ⟨hal-03017029⟩The theory of glassy fluctuations can be formulated in terms of disordered effective potentials. While the properties of the average potentials are well understood, the study of the fluctuations has been so far quite limited. Close to the MCT transition, fluctuations induced by the dynamical heterogeneities in supercooled liquids can be described by a cubic field theory in presence of a random field term. In this paper we set up the general problem of the large deviations going beyond the assumption of the vicinity to $T_{MCT}$ and analyze it in the paradigmatic case of spherical ($p$-spin) glass models. This tool can be applied to study the probability of the observation of a dynamics with memory of the initial condition in regimes where, typically, the correlation $C(t,0)$ decays to zero at long times, at finite $T$ and at $T=0$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Ising model with stochastic resetting – Archive ouverte HAL

### Matteo Magoni

^{1}Satya N. Majumdar^{1}Grégory Schehr^{1}#### Matteo Magoni, Satya N. Majumdar, Grégory Schehr. Ising model with stochastic resetting.

*Physical Review Research*, American Physical Society, 2020, 2 (3), ⟨10.1103/PhysRevResearch.2.033182⟩. ⟨hal-03010228⟩We study the stationary properties of the Ising model that, while evolving towards its equilibrium state at temperature $T$ according to the Glauber dynamics, is stochastically reset to its fixed initial configuration with magnetisation $m_0$ at a constant rate $r$. Resetting breaks detailed balance and drives the system to a non-equilibrium stationary state where the magnetisation acquires a nontrivial distribution, leading to a rich phase diagram in the $(T,r)$ plane. We establish these results exactly in one-dimension and present scaling arguments supported by numerical simulations in two-dimensions. We show that resetting gives rise to a novel "pseudo-ferro" phase in the $(T,r)$ plane for $r > r^*(T)$ and $T>T_c$ where $r^*(T)$ is a crossover line separating the pseudo-ferro phase from a paramagnetic phase. This pseudo-ferro phase is characterised by a non-zero typical magnetisation and a vanishing gap near $m=0$ of the magnetisation distribution.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Intermittent resetting potentials – Archive ouverte HAL

### Gabriel Mercado-VásquezDenis BoyerSatya N. Majumdar

^{1}Grégory Schehr^{1}#### Gabriel Mercado-Vásquez, Denis Boyer, Satya N. Majumdar, Grégory Schehr. Intermittent resetting potentials.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2020, 2020 (11), pp.113203. ⟨10.1088/1742-5468/abc1d9⟩. ⟨hal-03010255⟩We study the non-equilibrium steady states and first passage properties of a Brownian particle with position $X$ subject to an external confining potential of the form $V(X)=\mu|X|$, and that is switched on and off stochastically. Applying the potential intermittently generates a physically realistic diffusion process with stochastic resetting toward the origin, a topic which has recently attracted a considerable interest in a variety of theoretical contexts but has remained challenging to implement in lab experiments. The present system exhibits rich features, not observed in previous resetting models. The mean time needed by a particle starting from the potential minimum to reach an absorbing target located at a certain distance can be minimized with respect to the switch-on and switch-off rates. The optimal rates undergo continuous or discontinuous transitions as the potential strength $\mu$ is varied across non-trivial values. A discontinuous transition with metastable behavior is also observed for the optimal strength at fixed rates.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Human running performance from real-world big data – Archive ouverte HAL

### Thorsten Emig

^{1}Jussi Peltonen#### Thorsten Emig, Jussi Peltonen. Human running performance from real-world big data.

*Nature Communications*, Nature Publishing Group, 2020, 11 (1), ⟨10.1038/s41467-020-18737-6⟩. ⟨hal-03065483⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Freezing transition in the barrier crossing rate of a diffusing particle – Archive ouverte HAL

### Sanjib Sabhapandit

^{1}Satya N. Majumdar^{2}#### Sanjib Sabhapandit, Satya N. Majumdar. Freezing transition in the barrier crossing rate of a diffusing particle.

*Physical Review Letters*, American Physical Society, 2020. ⟨hal-03010264⟩We study the decay rate $\theta(a)$ that chracterizes the late time exponential decay of the first-passage probability density, $F_a(t|0) \sim e^{-\theta(a)\, t}$, of a diffusing particle in a one dimensional confining potential $U(x)$, starting from the origin, to a position located at $a>0$. For general confining potential $U(x)$ we show that $\theta(a)$, a measure of the barrier (located at $a$) crossing rate, has three distinct behaviors as a function of $a$, depending on the tail of $U(x)$ as $x\to -\infty$. In particular, for potentials behaving as $U(x)\sim |x|$ when $x\to -\infty$, we show that a novel freezing transition occurs at a critical value $a=a_c$, i.e, $\theta(a)$ increases monotonically as $a$ decreases till $a_c$, and for $a \le a_c$ it freezes to $\theta (a)=\theta(a_c)$. Our results are established using a general mapping to a quantum problem and by exact solution in three representative cases, supported by numerical simulations. We show that the freezing transition occurs when in the associated quantum problem, the gap between the ground state (bound) and the continuum of scattering states vanishes.

- 1. Raman Research Institute
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Formation of dispersive shock waves in a saturable nonlinear medium – Archive ouverte HAL

### Sergey K. IvanovJules-Elémir SuchorskiAnatoly M. KamchatnovMathieu Isoard

^{1}Nicolas Pavloff^{1}#### Sergey K. Ivanov, Jules-Elémir Suchorski, Anatoly M. Kamchatnov, Mathieu Isoard, Nicolas Pavloff. Formation of dispersive shock waves in a saturable nonlinear medium.

*Physical Review E*, American Physical Society (APS), 2020, 102 (3), ⟨10.1103/PhysRevE.102.032215⟩. ⟨hal-03017066⟩We use the Gurevich-Pitaevskii approach based on the Whitham averaging method for studying the formation of dispersive shock waves in an intense light pulse propagating through a saturable nonlinear medium. Although the Whitham modulation equations cannot be diagonalized in this case, the main characteristics of the dispersive shock can be derived by means of an analysis of the properties of these equations at the boundaries of the shock. Our approach generalizes a previous analysis of step-like initial intensity distributions to a more realistic type of initial light pulse and makes it possible to determine, in a setting of experimental interest, the value of measurable quantities such as the wave-breaking time or the position and light intensity of the shock edges.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Fluctuations of the Product of Random Matrices and Generalized Lyapunov Exponent – Archive ouverte HAL

### Christophe Texier

^{1}#### Christophe Texier. Fluctuations of the Product of Random Matrices and Generalized Lyapunov Exponent.

*Journal of Statistical Physics*, Springer Verlag, 2020, 181 (3), pp.990-1051. ⟨10.1007/s10955-020-02617-w⟩. ⟨hal-03017028⟩I present a general framework allowing to carry out explicit calculation of the moment generating function of random matrix products $\Pi_n=M_nM_{n-1}\cdots M_1$, where $M_i$'s are i.i.d.. Following Tutubalin [Theor. Probab. Appl. {\bf 10}, 15 (1965)], the calculation of the generating function is reduced to finding the largest eigenvalue of a certain transfer operator associated with a family of representations of the group. The formalism is illustrated by considering products of random matrices from the group $\mathrm{SL}(2,\mathbb{R})$ where explicit calculations are possible. For concreteness, I study in detail transfer matrix products for the one-dimensional Schr\"odinger equation where the random potential is a L\'evy noise (derivative of a L\'evy process). In this case, I obtain a general formula for the variance of $\ln||\Pi_n||$ and for the variance of $\ln|\psi(x)|$, where $\psi(x)$ is the wavefunction, in terms of a single integral involving the Fourier transform of the invariant density of the matrix product. Finally I discuss the continuum limit of random matrix products (matrices close to the identity ). In particular, I investigate a simple case where the spectral problem providing the generalized Lyapunov exponent can be solved exactly.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Finite-time adiabatic processes: Derivation and speed limit – Archive ouverte HAL

### Carlos Plata

^{1}David Guéry-Odelin^{2}Emmanuel Trizac^{3}Antonio Prados^{4}#### Carlos Plata, David Guéry-Odelin, Emmanuel Trizac, Antonio Prados. Finite-time adiabatic processes: Derivation and speed limit.

*Physical Review E*, American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032129⟩. ⟨hal-02535447⟩Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation.

- 1. Padova University
- 2. Atomes Froids (LCAR)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Universidad de Sevilla

## Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions – Archive ouverte HAL

### Etienne GranetMaurizio Fagotti

^{1}Fabian H.L. Essler#### Etienne Granet, Maurizio Fagotti, Fabian H.L. Essler. Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions.

*SciPost Phys.*, 2020, 9 (3), pp.033. ⟨10.21468/SciPostPhys.9.3.033⟩. ⟨hal-02542815⟩We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Few-body bound states of two-dimensional bosons – Archive ouverte HAL

### G. Guijarro

^{1}G. E. Astrakharchik^{1}J. Boronat^{1}B. BazakD. S. Petrov^{2}#### G. Guijarro, G. E. Astrakharchik, J. Boronat, B. Bazak, D. S. Petrov. Few-body bound states of two-dimensional bosons.

*Physical Review A*, American Physical Society 2020, ⟨10.1103/PhysRevA.101.041602⟩. ⟨hal-02537195⟩We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a two-dimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction switches to repulsion.

- 1. UPC - Universitat Politècnica de Catalunya [Barcelona]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Extreme value statistics of correlated random variables: a pedagogical review – Archive ouverte HAL

### Satya N. Majumdar

^{1}Arnab PalGregory Schehr^{1}#### Satya N. Majumdar, Arnab Pal, Gregory Schehr. Extreme value statistics of correlated random variables: a pedagogical review.

*Physics Reports*, Elsevier, 2020, ⟨10.10667⟩. ⟨hal-02512248⟩Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of `uncorrelated' variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this review, we will first recall the classical EVS for uncorrelated variables and discuss the three universality classes of extreme value limiting distribution, known as the Gumbel, Fr\'echet and Weibull distribution. We then show that, for weakly correlated random variables with a finite correlation length/time, the limiting extreme value distribution can still be inferred from that of the uncorrelated variables using a renormalisation group-like argument. Finally, we consider the most interesting examples of strongly correlated variables for which there are very few exact results for the EVS. We discuss few examples of such strongly correlated systems (such as the Brownian motion and the eigenvalues of a random matrix) where some analytical progress can be made. We also discuss other observables related to extremes, such as the density of near-extreme events, time at which an extreme value occurs, order and record statistics, etc.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Experimental Study of Collective Pedestrian Dynamics – Archive ouverte HAL

### Cécile Appert-RollandJulien PettréAnne-Hélène OlivierWilliam WarrenAymeric Duigou-MajumdarEtienne PinsardAlexandre Nicolas

^{1}#### Cécile Appert-Rolland, Julien Pettré, Anne-Hélène Olivier, William Warren, Aymeric Duigou-Majumdar, et al.. Experimental Study of Collective Pedestrian Dynamics.

*Collective Dynamics*, 2020, 5, pp.A109. ⟨10.17815/CD.2020.109⟩. ⟨hal-02992406⟩We report on two series of experiments, conducted in the frame of two different collaborations designed to study how pedestrians adapt their trajectories and velocities in groups or crowds. Strong emphasis is put on the motivations for the chosen protocols and the experimental implementation. The first series deals with pattern formation, interactions between pedestrians, and decision-making in pedestrian groups at low to medium densities. In particular, we show how pedestrians adapt their headways in single-file motion depending on the (prescribed) leader's velocity. The second series of experiments focuses on static crowds at higher densities, a situation that can be critical in real life and in which the pedestrians' choices of motion are strongly constrained sterically. More precisely, we study the crowd's response to its crossing by a pedestrian or a cylindrical obstacle of 74cm in diameter. In the latter case, for a moderately dense crowd, we observe displacements that quickly decay with the minimal distance to the obstacle, over a lengthscale of the order of the meter.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Engineered Swift Equilibration of brownian particles: consequences of hydrodynamic coupling – Archive ouverte HAL

### Salambô Dago

^{1}Benjamin Besga^{1}Raphaël Mothe^{1}David Guéry-Odelin^{2}Emmanuel Trizac^{3}Artyom Petrosyan^{1}Ludovic Bellon^{1}Sergio Ciliberto^{1}#### Salambô Dago, Benjamin Besga, Raphaël Mothe, David Guéry-Odelin, Emmanuel Trizac, et al.. Engineered Swift Equilibration of brownian particles: consequences of hydrodynamic coupling.

*SciPost Physics*, SciPost Foundation, 2020, 9 (5), ⟨10.21468/SciPostPhys.9.5.064⟩. ⟨ensl-02570537v2⟩We present a detailed theoretical and experimental analysis of Engineered Swift Equilibration (ESE) protocols applied to two hydrodynamically coupled colloids in optical traps. The second particle slightly perturbs (10% at most) the response to an ESE compression applied to a single particle. This effect is quantitatively explained by a model of hydrodynamic coupling. We then design a coupled ESE protocol for the two particles, allowing the perfect control of one target particle while the second is enslaved to the first. The calibration errors and the limitations of the model are finally discussed in details.

- 1. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 2. Atomes Froids (LCAR)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

### J. Ricardo G. Mendonça

^{1, 2}*Computational and Applied Mathematics*, Springer Verlag, 2020, 39 (3), ⟨10.1007/s40314-020-01295-4⟩. ⟨hal-03085042⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. USP - Universidade de São Paulo

## Distribution of the time between maximum and minimum of random walks – Archive ouverte HAL

### Francesco Mori

^{1}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Distribution of the time between maximum and minimum of random walks.

*Physical Review E*, American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052111⟩. ⟨hal-02881215⟩We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global minimum and the time $t_{\max}$ of the global maximum. We extend this result to a Brownian bridge, i.e. a periodic Brownian motion of period $T$. In both cases, we compute analytically the first few moments of $\tau$, as well as the covariance of $t_{\max}$ and $t_{\min}$, showing that these times are anti-correlated. We demonstrate that the distribution of $\tau$ for Brownian motion is valid for discrete-time random walks with $n$ steps and with a finite jump variance, in the limit $n\to \infty$. In the case of L\'evy flights, which have a divergent jump variance, we numerically verify that the distribution of $\tau$ differs from the Brownian case. For random walks with continuous and symmetric jumps we numerically verify that the probability of the event "$\tau = n$" is exactly $1/(2n)$ for any finite $n$, independently of the jump distribution. Our results can be also applied to describe the distance between the maximal and minimal height of $(1+1)$-dimensional stationary-state Kardar-Parisi-Zhang interfaces growing over a substrate of finite size $L$. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 123, 200201 (2019)].

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Dispersionless evolution of inviscid nonlinear pulses – Archive ouverte HAL

### M. Isoard

^{1}N. Pavloff^{1}A. M. Kamchatnov^{2}#### M. Isoard, N. Pavloff, A. M. Kamchatnov. Dispersionless evolution of inviscid nonlinear pulses.

*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020. ⟨hal-02565206⟩We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute of Spectroscopy

## Density scaling of generalized Lennard-Jones fluids in different dimensions – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Jeppe C. DyreLorenzo CostigliolaJeppe Dyre*SciPost Physics*, SciPost Foundation, 2020, 9 (6), ⟨10.21468/SciPostPhys.9.6.090⟩. ⟨hal-03117941⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Current fluctuations in noninteracting run-and-tumble particles in one dimension – Archive ouverte HAL

### Tirthankar Banerjee

^{1}Satya N. Majumdar^{1}Alberto Rosso^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Tirthankar Banerjee, Satya N. Majumdar, Alberto Rosso, Satya Majumdar, Gregory Schehr. Current fluctuations in noninteracting run-and-tumble particles in one dimension.

*Physical Review E*, American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052101⟩. ⟨hal-02565189⟩We present a general framework to study the distribution of the flux through the origin up to time $t$, in a non-interacting one-dimensional system of particles with a step initial condition with a fixed density $\rho$ of particles to the left of the origin. We focus principally on two cases: (i) when the particles undergo diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution both for the annealed and the quenched initial conditions, for the passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean $\mu(t)$ that we compute exactly in terms of the Green's function of the single particle dynamics. For the quenched case, we show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large deviation form at large times $P_{\rm qu}(Q,t) \sim \exp\left[-\rho\, v_0\, \gamma \, t^2 \psi_{\rm RTP}\left(\frac{Q}{\rho v_0\,t} \right) \right]$, where $\gamma$ is the rate of tumbling and $v_0$ is the ballistic speed between two successive tumblings. In this paper, we compute the rate function $\psi_{\rm RTP}(q)$ and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time $t$, there is no particle to the right of the origin. For diffusive and run-and-tumble dynamics, we find that this probability decays with time as a stretched exponential, $\sim \exp(-c\, \sqrt{t})$ where the constant $c$ can be computed exactly. We verify our results for these large deviations by using an importance sampling Monte-Carlo method.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Critical energy landscape of linear soft spheres – Archive ouverte HAL

### Silvio Franz

^{1}Antonio Sclocchi^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Critical energy landscape of linear soft spheres.

*SciPost Physics*, SciPost Foundation, 2020. ⟨hal-02908534⟩We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are non-linear, system spanning, and characterized by a set of non-trivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that self-organize into new, critical, marginally stable, states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Comment on “Effective Confining Potential of Quantum States in Disordered Media” – Archive ouverte HAL

### Alain Comtet

^{1}Christophe Texier^{1}#### Alain Comtet, Christophe Texier. Comment on “Effective Confining Potential of Quantum States in Disordered Media”.

*Physical Review Letters*, American Physical Society, 2020, 124 (21), ⟨10.1103/PhysRevLett.124.219701⟩. ⟨hal-02881221⟩We provide some analytical tests of the density of states estimation from the "localization landscape" approach of Ref. [Phys. Rev. Lett. 116, 056602 (2016)]. We consider two different solvable models for which we obtain the distribution of the landscape function and argue that the precise spectral singularities are not reproduced by the estimation of the landscape approach.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Collective excitations of a one-dimensional quantum droplet – Archive ouverte HAL

### Marek TylutkiGrigori E. AstrakharchikBoris A. Malomed

^{1}Dmitry S. Petrov^{2}Grigori Astrakharchik^{3}Boris Malomed^{4}Dmitry Petrov#### Marek Tylutki, Grigori E. Astrakharchik, Boris A. Malomed, Dmitry S. Petrov, Grigori Astrakharchik, et al.. Collective excitations of a one-dimensional quantum droplet.

*Physical Review A*, American Physical Society 2020, 101 (5), ⟨10.1103/PhysRevA.101.051601⟩. ⟨hal-02881226⟩We calculate the excitation spectrum of a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the mean-field energy of the mixture proportional to the effective coupling constant $\delta g$, whereas the quadratic nonlinearity corresponds to the attractive beyond-mean-field contribution. The droplet properties are governed by a control parameter $\gamma\propto \delta g N^{2/3}$, where $N$ is the particle number. For large $\gamma>0$ the droplet features the flat-top shape with the discrete part of its spectrum consisting of plane-wave Bogoliubov phonons propagating through the flat-density bulk and reflected by edges of the droplet. With decreasing $\gamma$ these modes cross into the continuum, sequentially crossing the particle-emission threshold at specific critical values. A notable exception is the breathing mode which we find to be always bound. The balance point $\gamma = 0$ provides implementation of a system governed by the GPE with an unusual quadratic nonlinearity. This case is characterized by the ratio of the breathing-mode frequency to the particle-emission threshold equal to 0.8904. As $\gamma$ tends to $-\infty$ this ratio tends to 1 and the droplet transforms into the soliton solution of the integrable cubic GPE.

- 1. Tel Aviv University [Tel Aviv]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. UPC - Universitat Politècnica de Catalunya [BarcelonaTech]
- 4. Department of Interdisciplinary Studies

### Ananyo Maitra

^{1}Martin Lenz^{2, 3}Raphael Voituriez^{1}*Physical Review Letters*, American Physical Society, 2020. ⟨hal-03085233⟩- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

## Chaos-assisted tunneling resonances in a synthetic Floquet superlattice – Archive ouverte HAL

### Maxime Arnal

^{1}Gabriel Chatelain^{1}Maxime Martinez^{2}Nathan Dupont^{1}Olivier Giraud^{3}D. Ullmo^{3}Bertrand Georgeot^{2}Gabriel Lemarié^{2}Juliette Billy^{1}David Guéry-Odelin^{1}#### Maxime Arnal, Gabriel Chatelain, Maxime Martinez, Nathan Dupont, Olivier Giraud, et al.. Chaos-assisted tunneling resonances in a synthetic Floquet superlattice.

*Science Advances*, 2020, 6 (38), pp.eabc4886. ⟨10.1126/sciadv.abc4886⟩. ⟨hal-02534927⟩The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the all-purpose quantum computer. In particular, the use of temporal driving has attracted a huge interest recently as it was shown that certain fast drivings can create new topological effects, while a strong driving leads to e.g. Anderson localization physics. In this work, we focus on the intermediate regime to observe a quantum chaos transport mechanism called chaos-assisted tunneling which provides new possibilities of control for quantum simulation. Indeed, this regime generates a rich classical phase space where stable trajectories form islands surrounded by a large sea of unstable chaotic orbits. This mimics an effective superlattice for the quantum states localized in the regular islands, with new controllable tunneling properties. Besides the standard textbook tunneling through a potential barrier, chaos-assisted tunneling corresponds to a much richer tunneling process where the coupling between quantum states located in neighboring regular islands is mediated by other states spread over the chaotic sea. This process induces sharp resonances where the tunneling rate varies by orders of magnitude over a short range of parameters. We experimentally demonstrate and characterize these resonances for the first time in a quantum system. This opens the way to new kinds of quantum simulations with long-range transport and new types of control of quantum systems through complexity.

- 1. Atomes Froids (LCAR)
- 2. Information et Chaos Quantiques (LPT)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator – Archive ouverte HAL

### Carlos A. PlataDavid Guéry-Odelin

^{1}Emmanuel Trizac^{2}Antonio Prados#### Carlos A. Plata, David Guéry-Odelin, Emmanuel Trizac, Antonio Prados. Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2020, 2020 (9), pp.093207. ⟨10.1088/1742-5468/abb0e1⟩. ⟨hal-03017062⟩We analyse non-equilibrium Carnot-like cycles built with a colloidal particle in a harmonic trap, which is immersed in a fluid that acts as a heat bath. Our analysis is carried out in the overdamped regime. The cycle comprises four branches: two isothermal processes and two \textit{locally} adiabatic ones. In the latter, both the temperature of the bath and the stiffness of the harmonic trap vary in time, but in such a way that the average heat vanishes for all times. All branches are swept at a finite rate and, therefore, the corresponding processes are irreversible, not quasi-static. Specifically, we are interested in optimising the heat engine to deliver the maximum power and characterising the corresponding values of the physical parameters. The efficiency at maximum power is shown to be very close to the Curzon-Ahlborn bound over the whole range of the ratio of temperatures of the two thermal baths, pointing to the near optimality of the proposed protocol.

- 1. Atomes Froids (LCAR)
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Brownian flights over a circle – Archive ouverte HAL

### Alexander VladimirovSenya ShlosmanSergei Nechaev

^{1}#### Alexander Vladimirov, Senya Shlosman, Sergei Nechaev. Brownian flights over a circle.

*Physical Review E*, American Physical Society (APS), 2020, 102 (1), ⟨10.1103/PhysRevE.102.012124⟩. ⟨hal-03009773⟩The stationary radial distribution, $P(\rho)$, of the random walk with the diffusion coefficient $D$, which winds with the tangential velocity $V$ around the impenetrable disc of radius $R$ for $R\gg 1$ converges to the distribution involving the Airy function. Typical trajectories are localized in the circular strip $[R, R+ \delta R^{1/3}]$, where $\delta$ is the constant which depends on the parameters $D$ and $V$ and is independent on $R$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Asymptotic behavior of the length of the longest increasing subsequences of random walks – Archive ouverte HAL

### J. Ricardo G. Mendonça

^{1}Hendrik Schawe^{2}Alexander K. Hartmann^{3}Alexander Hartmann#### J. Ricardo G. Mendonça, Hendrik Schawe, Alexander K. Hartmann, Alexander Hartmann. Asymptotic behavior of the length of the longest increasing subsequences of random walks.

*Physical Review E*, American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032102⟩. ⟨hal-02512208⟩We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$-distribution with parameter in the range $1/2 \leq \nu \leq 5$. We find that the expected value $\mathbb{E}(L_{n}) \sim n^{\theta}\ln{n}$ with $\theta$ decreasing from $\theta(\nu=1/2) \approx 0.70$ to $\theta(\nu \geq 5/2) \approx 0.50$. For random walks with distribution of step increments of finite variance ($\nu > 2$), this confirms previous observation of $\mathbb{E}(L_{n}) \sim \sqrt{n}\ln{n}$ to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of $\mathbb{E}(L_{n})$ for random walks with step increments of finite variance.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Oldenburg
- 3. Institut für Physik

## Archive ouverte HAL – Velocity and diffusion constant of an active particle in a one-dimensional force field

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}Gregory Schehr^{2}#### Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Velocity and diffusion constant of an active particle in a one-dimensional force field.

*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020, 130 (4), pp.40002. ⟨10.1209/0295-5075/130/40002⟩. ⟨hal-02881224⟩We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of period $L$. They involve the "active potential" which allows to define a global bias. Upon varying parameters, such as an external force $F$, the dynamics undergoes transitions from non-ergodic trapped states, to various moving states, some with non analyticities in the $V_L$ versus $F$ curve. A random landscape in the presence of a bias leads, for large $L$, to anomalous diffusion $x \sim t^\mu$, $\mu<1$, or to a phase with a finite velocity that we calculate.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle

### Francesco Mori

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle.

*Physical Review Letters*, American Physical Society, 2020, 124 (9), ⟨10.1103/PhysRevLett.124.090603⟩. ⟨hal-02512214⟩We consider an active run-and-tumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$-component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Champs Aléatoires et Systèmes hors d'Équilibre

## Archive ouverte HAL – Universal Scaling of the Velocity Field in Crack Front Propagation

### Clément Le Priol

^{1}Pierre Le Doussal^{2}Laurent Ponson^{3}Alberto Rosso^{4}Julien Chopin^{5}#### Clément Le Priol, Pierre Le Doussal, Laurent Ponson, Alberto Rosso, Julien Chopin. Universal Scaling of the Velocity Field in Crack Front Propagation.

*Physical Review Letters*, American Physical Society, 2020, 124 (6), ⟨10.1103/PhysRevLett.124.065501⟩. ⟨hal-02512228⟩The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.

- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. Champs Aléatoires et Systèmes hors d'Équilibre
- 3. DALEMBERT - Institut Jean Le Rond d'Alembert
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. IF-UFB - Instituto de Fisica, Universidade Federal da Bahia

## Archive ouverte HAL – Universal gap statistics for random walks for a class of jump densities

### Matteo Battilana

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}#### Matteo Battilana, Satya N. Majumdar, Gregory Schehr. Universal gap statistics for random walks for a class of jump densities.

*Markov Processes And Related Fields*, Polymat Publishing Company, 2020. ⟨hal-02518812⟩We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim |\eta|^p \,e^{-|\eta|}$, parametrized by a non-negative integer $p$. Our main focus is on the statistics of the gaps $d_{k,n}$ between two successive maxima $d_{k,n}=M_{k,n}-M_{k+1,n}$ where $M_{k,n}$ is the $k$-th maximum of the RW between step 1 and step $n$. In the limit of large $n$, we show that the probability density function of the gaps $P_{k,n}(\Delta) = \Pr(d_{k,n} = \Delta)$ reaches a stationary density $P_{k,n}(\Delta) \to p_k(\Delta)$. For large $k$, we demonstrate that the typical fluctuations of the gap, for $d_{k,n}= O(1/\sqrt{k})$ (and $n \to \infty$), are described by a non-trivial scaling function that is independent of $k$ and of the jump probability density function $f_p(\eta)$, thus corroborating our conjecture about the universality of the regime of typical fluctuations (see G. Schehr, S. N. Majumdar, Phys. Rev. Lett. 108, 040601 (2012)). We also investigate the large fluctuations of the gap, for $d_{k,n} = O(1)$ (and $n \to \infty$), and show that these two regimes of typical and large fluctuations of the gaps match smoothly.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Two anyons on the sphere: nonlinear states and spectrum

### Alexios P. PolychronakosStéphane Ouvry

^{1}#### Alexios P. Polychronakos, Stéphane Ouvry. Two anyons on the sphere: nonlinear states and spectrum.

*Nucl.Phys.B*, 2020, 951, pp.114906. ⟨10.1016/j.nuclphysb.2019.114906⟩. ⟨hal-02340259⟩We study the energy spectrum of two anyons on the sphere in a constant magnetic field. Making use of rotational invariance we reduce the energy eigenvalue equation to a system of linear differential equations for functions of a single variable, a reduction analogous to separating center of mass and relative coordinates on the plane. We solve these equations by a generalization of the Frobenius method and derive numerical results for the energies of non-analytically derivable states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus

### Nina Javerzat

^{1}Marco Picco^{2}Raoul Santachiara^{1}#### Nina Javerzat, Marco Picco, Raoul Santachiara. Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus.

*J.Stat.Mech.*, 2020, 2005, pp.053106. ⟨10.1088/1742-5468/ab7c5e⟩. ⟨hal-02416915⟩In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of Q-Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work by considering the torus corrections to the three- and four-point connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other non-trivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies

## Archive ouverte HAL – The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

### Giuseppe Petrillo

^{1}Eugenio Lippiello^{1}François Landes^{2}Alberto Rosso^{3}#### Giuseppe Petrillo, Eugenio Lippiello, François Landes, Alberto Rosso. The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence.

*Nature Communications*, Nature Publishing Group, 2020. ⟨hal-02908552⟩Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.

- 1. Department of Mathematics and Physics [Caserta]
- 2. LRI - Laboratoire de Recherche en Informatique
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The convex hull of the run-and-tumble particle in a plane

### Alexander K HartmannSatya N Majumdar

^{1}Hendrik Schawe^{2}Gregory Schehr^{1}Alexander Hartmann^{2}Satya Majumdar^{1}#### Alexander K Hartmann, Satya N Majumdar, Hendrik Schawe, Gregory Schehr, Alexander Hartmann, et al.. The convex hull of the run-and-tumble particle in a plane.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2020, 2020 (5), pp.053401. ⟨10.1088/1742-5468/ab7c5f⟩. ⟨hal-02881103⟩We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its direction randomly. We consider two different statistical ensembles where we either fix (i) the total number of tumblings $n$ or (ii) the total duration $t$ of the time interval. In both cases, we derive exact expressions for the average perimeter of the convex hull and then compare to numerical estimates finding excellent agreement. Further, we numerically compute the full distribution of the perimeter using Markov chain Monte Carlo techniques, in both ensembles, probing the far tails of the distribution, up to a precision smaller than $10^{-100}$. This also allows us to characterize the rare events that contribute to the tails of these distributions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Oldenburg

## Archive ouverte HAL – Symmetries in $B \to D^* \ell \nu$ angular observables

### Marcel AlgueróSébastien Descotes-Genon

^{1}Joaquim MatiasMartín Novoa-Brunet^{2}#### Marcel Algueró, Sébastien Descotes-Genon, Joaquim Matias, Martín Novoa-Brunet. Symmetries in $B \to D^* \ell \nu$ angular observables.

*JHEP*, 2020, 06, pp.156. ⟨10.1007/JHEP06(2020)156⟩. ⟨hal-02518081⟩We apply the formalism of amplitude symmetries to the angular distribution of the decays B → D$^{∗}$ℓν for ℓ = e, μ, τ . We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the D$^{∗}$ using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure $ {F}_L^{D\ast } $ in B → D$^{∗}$τν and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify three observables which may exhibit a tension if the experimental value of $ {F}_L^{D\ast } $ remains high. We discuss how these relations can be exploited for binned measurements. We also propose a new observable that could test for specific scenarios of New Physics generated by light right-handed neutrinos. Finally we study the prospects of testing these relations based on the projected experimental sensitivity of new experiments.

- 1. IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order

### Ananyo Maitra

^{1, 2}Pragya SrivastavaM. Cristina MarchettiSriram RamaswamyMartin Lenz^{2, 3}#### Ananyo Maitra, Pragya Srivastava, M. Cristina Marchetti, Sriram Ramaswamy, Martin Lenz. Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order.

*Phys.Rev.Lett.*, 2020, 124 (2), pp.028002. ⟨10.1103/PhysRevLett.124.028002⟩. ⟨hal-02475283⟩We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations, not parallel to the ordering direction, at zero wave number. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature 503, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability.

- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. ESPCI ParisTech

## Archive ouverte HAL – Stochastic growth in time-dependent environments

### Guillaume Barraquand

^{1}Pierre Le Doussal^{1}Alberto Rosso^{2}#### Guillaume Barraquand, Pierre Le Doussal, Alberto Rosso. Stochastic growth in time-dependent environments.

*Physical Review E*, American Physical Society (APS), 2020, 101 (4), ⟨10.1103/PhysRevE.101.040101⟩. ⟨hal-02565202⟩We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{-\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution saturates at large times towards a non-universal limiting distribution. When $\alpha<1/2$ the fluctuation field is governed by scaling exponents depending on $\alpha$ and the limiting statistics are similar to the case when $c(t)$ is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential (2) An exactly solvable discretization, the log-gamma polymer model (3) Numerical simulations.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Statistics of first-passage Brownian functionals

### Satya N. Majumdar

^{1}Baruch Meerson#### Satya N. Majumdar, Baruch Meerson. Statistics of first-passage Brownian functionals.

*J.Stat.Mech.*, 2020, 2002 (2), pp.023202. ⟨10.1088/1742-5468/ab6844⟩. ⟨hal-02497830⟩We study the distribution of first-passage functionals of the type where represents a Brownian motion (with or without drift) with diffusion constant D, starting at x 0 > 0, and t f is the first-passage time to the origin. In the driftless case, we compute exactly, for all n > −2, the probability density . We show that has an essential singular tail as and a power-law tail as . The leading essential singular behavior for small A can be obtained using the optimal fluctuation method (OFM), which also predicts the optimal paths of the conditioned process in this limit. For the case with a drift toward the origin, where no exact solution is known for general n > −1, we show that the OFM successfully predicts the tails of the distribution. For it predicts the same essential singular tail as in the driftless case. For it predicts a stretched exponential tail for all n > 0. In the limit of large Péclet number , where is the drift velocity toward the origin, the OFM predicts an exact large-deviation scaling behavior, valid for all A: , where is the mean value of in this limit. We compute the rate function analytically for all n > −1. We show that, while for n > 0 the rate function is analytic for all z, it has a non-analytic behavior at z = 1 for −1 < n < 0 which can be interpreted as a dynamical phase transition. The order of this transition is 2 for −1/2 < n < 0, while for −1 < n < −1/2 the order of transition is ; it changes continuously with n. We also provide an illuminating alternative derivation of the OFM result by using a WKB-type asymptotic perturbation theory for large . Finally, we employ the OFM to study the case of (drift away from the origin). We show that, when the process is conditioned on reaching the origin, the distribution of coincides with the distribution of for with the same .

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – State transition graph of the Preisach model and the role of return-point memory

### M. Mert Terzi

^{1}Muhittin Mungan#### M. Mert Terzi, Muhittin Mungan. State transition graph of the Preisach model and the role of return-point memory.

*Physical Review E*, 2020, 102 (1), ⟨10.1103/PhysRevE.102.012122⟩. ⟨hal-02908545⟩The Preisach model has been useful as a null-model for understanding memory formation in periodically driven disordered systems. In amorphous solids for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by one of us, the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between soft-spots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying soft-spot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return point memory in organizing the graph into a hierarchy of loops and sub-loops. Our analysis reveals that the topology of a large portion of this graph is actually not governed by the values of the switching fields that describe the individual hysteretic behavior of the individual elements, but by a coarser parameter, a permutation $\rho$ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states $| \mathcal{R} |$ constituting the main hysteresis loop and its nested subloops. We find that $| \mathcal{R} |$ is equal to the number of increasing subsequences contained in the permutation $\rho$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Scalable quantum computing with qudits on a graph

### E. O. Kiktenko

^{1}A. S. NikolaevaPeng XuG. V. Shlyapnikov^{2}A. K. Fedorov^{3}#### E. O. Kiktenko, A. S. Nikolaeva, Peng Xu, G. V. Shlyapnikov, A. K. Fedorov. Scalable quantum computing with qudits on a graph.

*Physical Review A*, American Physical Society 2020, 101 (2), ⟨10.1103/PhysRevA.101.022304⟩. ⟨hal-02512218⟩We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multi-qudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.

- 1. IPE - Schmidt United Institute of Physics of the Earth [Moscow]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Russian Quantum Center

## Archive ouverte HAL – Reversal of contractility as a signature of self-organization in cytoskeletal bundles

### Martin Lenz

^{1}#### Martin Lenz. Reversal of contractility as a signature of self-organization in cytoskeletal bundles.

*eLife*, eLife Sciences Publication, 2020, 9, ⟨10.7554/eLife.51751⟩. ⟨hal-02518848⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Optimizing Brownian escape rates by potential shaping

### Marie Chupeau

^{1}Jannes GladrowAlexei Chepelianskii^{2}Ulrich F. KeyserEmmanuel Trizac^{1}Ulrich Keyser#### Marie Chupeau, Jannes Gladrow, Alexei Chepelianskii, Ulrich F. Keyser, Emmanuel Trizac, et al.. Optimizing Brownian escape rates by potential shaping.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2020, 117 (3), pp.1383-1388. ⟨10.1073/pnas.1910677116⟩. ⟨hal-02512216⟩Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under two different regularizations, and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPCT - Laboratoire de Physico-Chimie Théorique

## Archive ouverte HAL – Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

### John MartinStefan WeigertOlivier Giraud

^{1}#### John Martin, Stefan Weigert, Olivier Giraud. Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States.

*Quantum*, Verein, 2020. ⟨hal-02881098⟩Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids

### Alessandro Manacorda

^{1}Gregory Schehr^{2}Francesco Zamponi^{1}#### Alessandro Manacorda, Gregory Schehr, Francesco Zamponi. Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids.

*Journal of Chemical Physics*, American Institute of Physics, 2020, 152 (16), pp.164506. ⟨10.1063/5.0007036⟩. ⟨hal-02554137⟩- 1. Systèmes Désordonnés et Applications
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Noninteracting trapped Fermions in double-well potentials: inverted parabola kernel

### Naftali R. Smith

^{1}David S. Dean^{2}Pierre Le Doussal^{3}Satya N. Majumdar^{1}Grégory Schehr^{1}#### Naftali R. Smith, David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr. Noninteracting trapped Fermions in double-well potentials: inverted parabola kernel.

*Phys.Rev.A*, 2020, 101 (5), pp.053602. ⟨10.1103/PhysRevA.101.053602⟩. ⟨hal-02484003⟩We study a system of N noninteracting spinless fermions in a confining double-well potential in one dimension. We show that when the Fermi energy is close to the value of the potential at its local maximum, physical properties, such as the average density and the fermion position correlation functions, display a universal behavior that depends only on the local properties of the potential near its maximum. This behavior describes the merging of two Fermi gases, which are disjoint at sufficiently low Fermi energies. We describe this behavior in terms of a correlation kernel that we compute analytically and we call it the inverted parabola kernel. As an application, we calculate the mean and variance of the number of particles in an interval of size 2L centered around the position of the local maximum, for sufficiently small L. We discuss the possibility of observing our results in experiments, as well as extensions to nonzero temperature and to higher space dimensions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 3. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Multi-component colloidal gels: interplay between structure and mechanical properties

### Claudia Ferreiro-CordovaMehdi Bouzid

^{1}Emanuela del GadoGiuseppe Foffi^{2}Claudia Ferreiro-Córdova#### Claudia Ferreiro-Cordova, Mehdi Bouzid, Emanuela del Gado, Giuseppe Foffi, Claudia Ferreiro-Córdova. Multi-component colloidal gels: interplay between structure and mechanical properties.

*Soft Matter*, Royal Society of Chemistry, 2020, 16 (18), pp.4414-4421. ⟨10.1039/C9SM02410G⟩. ⟨hal-02881157⟩We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of component leads to softer solids that can accomodate progressively larger strain before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work {provides new insight into mechanisms at play for controlling the material properties and open the road to new design principles for} soft composite solids

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Archive ouverte HAL – Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes

### Guillaume Lamour

^{1}Antoine Allard^{1, 2}Juan Pelta^{1}Sid Labdi^{1}Martin Lenz^{3}Clément Campillo^{1}#### Guillaume Lamour, Antoine Allard, Juan Pelta, Sid Labdi, Martin Lenz, et al.. Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes.

*Physical Review X*, American Physical Society, 2020, 10 (1), pp.011031. ⟨10.1103/PhysRevX.10.011031⟩. ⟨hal-02512272⟩Membrane nanotubes are continuously assembled and disassembled by the cell to generate and dispatch transport vesicles, for instance, in endocytosis. While these processes crucially involve the ill-understood local mechanics of the nanotube, existing micromanipulation assays only give access to its global mechanical properties. Here we develop a new platform to study this local mechanics using atomic force microscopy (AFM). On a single coverslip we quickly generate millions of substrate-bound nanotubes, out of which dozens can be imaged by AFM in a single experiment. A full theoretical description of the AFM tip-membrane interaction allows us to accurately relate AFM measurements of the nanotube heights, widths, and rigidities to the membrane bending rigidity and tension, thus demonstrating our assay as an accurate probe of nanotube mechanics. We reveal a universal relationship between nanotube height and rigidity, which is unaffected by the specific conditions of attachment to the substrate. Moreover, we show that the parabolic shape of force-displacement curves results from thermal fluctuations of the membrane that collides intermittently with the AFM tip. We also show that membrane nanotubes can exhibit high resilience against extreme lateral compression. Finally, we mimic in vivo actin polymerization on nanotubes and use AFM to assess the induced changes in nanotube physical properties. Our assay may help unravel the local mechanics of membrane-protein interactions, including membrane remodeling in nanotube scission and vesicle formation.

- 1. LAMBE - UMR 8587 - Laboratoire Analyse, Modélisation et Matériaux pour la Biologie et l'Environnement
- 2. PCC - Physico-Chimie-Curie
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Locally quasi-stationary states in noninteracting spin chains

### Maurizio Fagotti

^{1}#### Maurizio Fagotti. Locally quasi-stationary states in noninteracting spin chains.

*SciPost Phys.*, 2020, 8, pp.048. ⟨10.21468/SciPostPhys.8.3.048⟩. ⟨hal-02423699⟩Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Finite-time adiabatic processes: Derivation and speed limit

### Carlos Plata

^{1}David Guéry-Odelin^{2}Emmanuel Trizac^{3}Antonio Prados^{4}#### Carlos Plata, David Guéry-Odelin, Emmanuel Trizac, Antonio Prados. Finite-time adiabatic processes: Derivation and speed limit.

*Physical Review E*, American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032129⟩. ⟨hal-02535447⟩Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation.

- 1. Padova University
- 2. Atomes Froids (LCAR)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Universidad de Sevilla

## Archive ouverte HAL – Few-body bound states of two-dimensional bosons

### G. Guijarro

^{1}G. E. Astrakharchik^{1}J. Boronat^{1}B. BazakD. S. Petrov^{2}#### G. Guijarro, G. E. Astrakharchik, J. Boronat, B. Bazak, D. S. Petrov. Few-body bound states of two-dimensional bosons.

*Physical Review A*, American Physical Society 2020, ⟨10.1103/PhysRevA.101.041602⟩. ⟨hal-02537195⟩We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a two-dimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction switches to repulsion.

- 1. UPC - Universitat Politècnica de Catalunya [Barcelona]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Extreme value statistics of correlated random variables: a pedagogical review

### Satya N. Majumdar

^{1}Arnab PalGregory Schehr^{1}#### Satya N. Majumdar, Arnab Pal, Gregory Schehr. Extreme value statistics of correlated random variables: a pedagogical review.

*Physics Reports*, Elsevier, 2020, ⟨10.10667⟩. ⟨hal-02512248⟩Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of `uncorrelated' variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this review, we will first recall the classical EVS for uncorrelated variables and discuss the three universality classes of extreme value limiting distribution, known as the Gumbel, Fr\'echet and Weibull distribution. We then show that, for weakly correlated random variables with a finite correlation length/time, the limiting extreme value distribution can still be inferred from that of the uncorrelated variables using a renormalisation group-like argument. Finally, we consider the most interesting examples of strongly correlated variables for which there are very few exact results for the EVS. We discuss few examples of such strongly correlated systems (such as the Brownian motion and the eigenvalues of a random matrix) where some analytical progress can be made. We also discuss other observables related to extremes, such as the density of near-extreme events, time at which an extreme value occurs, order and record statistics, etc.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Dynamical Heart Beat Correlations during Running

### Matti MolkkariGiorgio Angelotti

^{1}Thorsten Emig^{1}Esa Rasanen^{1}#### Matti Molkkari, Giorgio Angelotti, Thorsten Emig, Esa Rasanen. Dynamical Heart Beat Correlations during Running.

*Sci.Rep.*, 2020, 10, pp.13627. ⟨10.1038/s41598-020-70358-7⟩. ⟨hal-02423731⟩Fluctuations of the human heart beat constitute a complex system that has been studied mostly under resting conditions using conventional time series analysis methods. During physical exercise, the variability of the fluctuations is reduced, and the time series of beat-to-beat RR intervals (RRIs) become highly non-stationary. Here we develop a dynamical approach to analyze the time evolution of RRI correlations in running across various training and racing events under real-world conditions. In particular, we introduce dynamical detrended fluctuation analysis and dynamical partial autocorrelation functions, which are able to detect real-time changes in the scaling and correlations of the RRIs as functions of the scale and the lag. We relate these changes to the exercise intensity quantified by the heart rate (HR). Beyond subject-specific HR thresholds the RRIs show multiscale anticorrelations with both universal and individual scale-dependent structure that is potentially affected by the stride frequency. These preliminary results are encouraging for future applications of the dynamical statistical analysis in exercise physiology and cardiology, and the presented methodology is also applicable across various disciplines.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Distribution of the time between maximum and minimum of random walks

### Francesco Mori

^{1}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Distribution of the time between maximum and minimum of random walks.

*Physical Review E*, American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052111⟩. ⟨hal-02881215⟩We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global minimum and the time $t_{\max}$ of the global maximum. We extend this result to a Brownian bridge, i.e. a periodic Brownian motion of period $T$. In both cases, we compute analytically the first few moments of $\tau$, as well as the covariance of $t_{\max}$ and $t_{\min}$, showing that these times are anti-correlated. We demonstrate that the distribution of $\tau$ for Brownian motion is valid for discrete-time random walks with $n$ steps and with a finite jump variance, in the limit $n\to \infty$. In the case of L\'evy flights, which have a divergent jump variance, we numerically verify that the distribution of $\tau$ differs from the Brownian case. For random walks with continuous and symmetric jumps we numerically verify that the probability of the event "$\tau = n$" is exactly $1/(2n)$ for any finite $n$, independently of the jump distribution. Our results can be also applied to describe the distance between the maximal and minimal height of $(1+1)$-dimensional stationary-state Kardar-Parisi-Zhang interfaces growing over a substrate of finite size $L$. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 123, 200201 (2019)].

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Dispersionless evolution of inviscid nonlinear pulses

### M. Isoard

^{1}N. Pavloff^{1}A. M. Kamchatnov^{2}#### M. Isoard, N. Pavloff, A. M. Kamchatnov. Dispersionless evolution of inviscid nonlinear pulses.

*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020. ⟨hal-02565206⟩We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute of Spectroscopy

## Archive ouverte HAL – Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate

### M. Isoard

^{1}N. Pavloff^{1}#### M. Isoard, N. Pavloff. Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate.

*Phys.Rev.Lett.*, 2020, 124 (6), pp.060401. ⟨10.1103/PhysRevLett.124.060401⟩. ⟨hal-02317273⟩We study the quantum fluctuations in a one-dimensional Bose-Einstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Current fluctuations in noninteracting run-and-tumble particles in one dimension

### Tirthankar Banerjee

^{1}Satya N. Majumdar^{1}Alberto Rosso^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Tirthankar Banerjee, Satya N. Majumdar, Alberto Rosso, Satya Majumdar, Gregory Schehr. Current fluctuations in noninteracting run-and-tumble particles in one dimension.

*Physical Review E*, American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052101⟩. ⟨hal-02565189⟩We present a general framework to study the distribution of the flux through the origin up to time $t$, in a non-interacting one-dimensional system of particles with a step initial condition with a fixed density $\rho$ of particles to the left of the origin. We focus principally on two cases: (i) when the particles undergo diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution both for the annealed and the quenched initial conditions, for the passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean $\mu(t)$ that we compute exactly in terms of the Green's function of the single particle dynamics. For the quenched case, we show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large deviation form at large times $P_{\rm qu}(Q,t) \sim \exp\left[-\rho\, v_0\, \gamma \, t^2 \psi_{\rm RTP}\left(\frac{Q}{\rho v_0\,t} \right) \right]$, where $\gamma$ is the rate of tumbling and $v_0$ is the ballistic speed between two successive tumblings. In this paper, we compute the rate function $\psi_{\rm RTP}(q)$ and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time $t$, there is no particle to the right of the origin. For diffusive and run-and-tumble dynamics, we find that this probability decays with time as a stretched exponential, $\sim \exp(-c\, \sqrt{t})$ where the constant $c$ can be computed exactly. We verify our results for these large deviations by using an importance sampling Monte-Carlo method.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Critical energy landscape of linear soft spheres

### Silvio Franz

^{1}Antonio Sclocchi^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Critical energy landscape of linear soft spheres.

*SciPost Physics*, SciPost Foundation, 2020. ⟨hal-02908534⟩We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are non-linear, system spanning, and characterized by a set of non-trivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that self-organize into new, critical, marginally stable, states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Archive ouverte HAL – Comment on “Effective Confining Potential of Quantum States in Disordered Media”

### Alain Comtet

^{1}Christophe Texier^{1}#### Alain Comtet, Christophe Texier. Comment on “Effective Confining Potential of Quantum States in Disordered Media”.

*Physical Review Letters*, American Physical Society, 2020, 124 (21), ⟨10.1103/PhysRevLett.124.219701⟩. ⟨hal-02881221⟩We provide some analytical tests of the density of states estimation from the "localization landscape" approach of Ref. [Phys. Rev. Lett. 116, 056602 (2016)]. We consider two different solvable models for which we obtain the distribution of the landscape function and argue that the precise spectral singularities are not reproduced by the estimation of the landscape approach.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Collective excitations of a one-dimensional quantum droplet

### Marek TylutkiGrigori E. AstrakharchikBoris A. Malomed

^{1}Dmitry S. Petrov^{2}Grigori Astrakharchik^{3}Boris Malomed^{4}Dmitry Petrov#### Marek Tylutki, Grigori E. Astrakharchik, Boris A. Malomed, Dmitry S. Petrov, Grigori Astrakharchik, et al.. Collective excitations of a one-dimensional quantum droplet.

*Physical Review A*, American Physical Society 2020, 101 (5), ⟨10.1103/PhysRevA.101.051601⟩. ⟨hal-02881226⟩We calculate the excitation spectrum of a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the mean-field energy of the mixture proportional to the effective coupling constant $\delta g$, whereas the quadratic nonlinearity corresponds to the attractive beyond-mean-field contribution. The droplet properties are governed by a control parameter $\gamma\propto \delta g N^{2/3}$, where $N$ is the particle number. For large $\gamma>0$ the droplet features the flat-top shape with the discrete part of its spectrum consisting of plane-wave Bogoliubov phonons propagating through the flat-density bulk and reflected by edges of the droplet. With decreasing $\gamma$ these modes cross into the continuum, sequentially crossing the particle-emission threshold at specific critical values. A notable exception is the breathing mode which we find to be always bound. The balance point $\gamma = 0$ provides implementation of a system governed by the GPE with an unusual quadratic nonlinearity. This case is characterized by the ratio of the breathing-mode frequency to the particle-emission threshold equal to 0.8904. As $\gamma$ tends to $-\infty$ this ratio tends to 1 and the droplet transforms into the soliton solution of the integrable cubic GPE.

- 1. Tel Aviv University [Tel Aviv]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. UPC - Universitat Politècnica de Catalunya [BarcelonaTech]
- 4. Department of Interdisciplinary Studies

## Archive ouverte HAL – Asymptotic behavior of the length of the longest increasing subsequences of random walks

### J. Ricardo G. Mendonça

^{1}Hendrik Schawe^{2}Alexander K. Hartmann^{3}Alexander Hartmann#### J. Ricardo G. Mendonça, Hendrik Schawe, Alexander K. Hartmann, Alexander Hartmann. Asymptotic behavior of the length of the longest increasing subsequences of random walks.

*Physical Review E*, American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032102⟩. ⟨hal-02512208⟩We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$-distribution with parameter in the range $1/2 \leq \nu \leq 5$. We find that the expected value $\mathbb{E}(L_{n}) \sim n^{\theta}\ln{n}$ with $\theta$ decreasing from $\theta(\nu=1/2) \approx 0.70$ to $\theta(\nu \geq 5/2) \approx 0.50$. For random walks with distribution of step increments of finite variance ($\nu > 2$), this confirms previous observation of $\mathbb{E}(L_{n}) \sim \sqrt{n}\ln{n}$ to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of $\mathbb{E}(L_{n})$ for random walks with step increments of finite variance.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Oldenburg
- 3. Institut für Physik

## Archive ouverte HAL – Actin modulates shape and mechanics of tubular membranes

### A. Allard

^{1}M. Bouzid^{2}T. Betz^{3}C. SimonM. Abou-GhaliJ. Lemiere^{4}F. Valentino^{5}J. Manzi^{4}F. Brochard-Wyart^{6}K. Guevorkian^{6}J. Plastino^{6}M. Lenz^{2}C. Campillo^{7}C. Sykes^{6}#### A. Allard, M. Bouzid, T. Betz, C. Simon, M. Abou-Ghali, et al.. Actin modulates shape and mechanics of tubular membranes.

*Science Advances*, American Association for the Advancement of Science (AAAS), 2020, 6 (17), pp.eaaz3050. ⟨10.1126/sciadv.aaz3050⟩. ⟨hal-02565199⟩- 1. LNE - Laboratoire National de Métrologie et d'Essais [Trappes]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Atominstitut
- 4. PCC - Physico-Chimie-Curie
- 5. DTU Space - National Space Institute [Lyngby]
- 6. PCC - Physico-Chimie-Curie
- 7. inconnu

## Actin modulates shape and mechanics of tubular membranes – Archive ouverte HAL

### A. Allard

^{1}M. Bouzid^{2}T. Betz^{3}C. SimonM. Abou-GhaliJ. Lemiere^{4}F. Valentino^{5}J. Manzi^{4}F. Brochard-Wyart^{6}K. Guevorkian^{6}J. Plastino^{6}M. Lenz^{2}C. Campillo^{7}C. Sykes^{6}#### A. Allard, M. Bouzid, T. Betz, C. Simon, M. Abou-Ghali, et al.. Actin modulates shape and mechanics of tubular membranes.

*Science Advances*, American Association for the Advancement of Science (AAAS), 2020, 6 (17), pp.eaaz3050. ⟨10.1126/sciadv.aaz3050⟩. ⟨hal-02565199⟩- 1. LNE - Laboratoire National de Métrologie et d'Essais [Trappes]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Atominstitut
- 4. PCC - Physico-Chimie-Curie
- 5. DTU Space - National Space Institute [Lyngby]
- 6. PCC - Physico-Chimie-Curie
- 7. inconnu

## Integrability and duality in spin chains – Archive ouverte HAL

### Eyzo StoutenPieter W. ClaeysJean-Sébastien CauxVladimir Gritsev

^{1}#### Eyzo Stouten, Pieter W. Claeys, Jean-Sébastien Caux, Vladimir Gritsev. Integrability and duality in spin chains.

*Phys.Rev.B*, 2019, 99 (7), pp.075111. ⟨10.1103/PhysRevB.99.075111⟩. ⟨hal-03171537⟩We construct a two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect noninteracting modes of different models. We apply this solution and duality to a Richardson-Gaudin model and generate a novel integrable system termed the s-d wave Richardson-Gaudin-Kitaev interacting chain, interpolating s- and d-wave superconductivity. The phase diagram of this interacting model has a topological phase transition that can be connected to the duality, where the occupancy of the noninteracting mode serves as a topological order parameter.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Integrability and duality in spin chains – Archive ouverte HAL

### Eyzo StoutenPieter W. ClaeysJean-Sébastien CauxVladimir Gritsev

^{1}#### Eyzo Stouten, Pieter W. Claeys, Jean-Sébastien Caux, Vladimir Gritsev. Integrability and duality in spin chains.

*Phys.Rev.B*, 2019, 99 (7), pp.075111. ⟨10.1103/PhysRevB.99.075111⟩. ⟨hal-03171537⟩We construct a two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect noninteracting modes of different models. We apply this solution and duality to a Richardson-Gaudin model and generate a novel integrable system termed the s-d wave Richardson-Gaudin-Kitaev interacting chain, interpolating s- and d-wave superconductivity. The phase diagram of this interacting model has a topological phase transition that can be connected to the duality, where the occupancy of the noninteracting mode serves as a topological order parameter.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Integrability and duality in spin chains – Archive ouverte HAL

### Eyzo StoutenPieter W. ClaeysJean-Sébastien CauxVladimir Gritsev

^{1}#### Eyzo Stouten, Pieter W. Claeys, Jean-Sébastien Caux, Vladimir Gritsev. Integrability and duality in spin chains.

*Phys.Rev.B*, 2019, 99 (7), pp.075111. ⟨10.1103/PhysRevB.99.075111⟩. ⟨hal-03171537⟩We construct a two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect noninteracting modes of different models. We apply this solution and duality to a Richardson-Gaudin model and generate a novel integrable system termed the s-d wave Richardson-Gaudin-Kitaev interacting chain, interpolating s- and d-wave superconductivity. The phase diagram of this interacting model has a topological phase transition that can be connected to the duality, where the occupancy of the noninteracting mode serves as a topological order parameter.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Integrability and duality in spin chains – Archive ouverte HAL

### Eyzo StoutenPieter W. ClaeysJean-Sébastien CauxVladimir Gritsev

^{1}*Phys.Rev.B*, 2019, 99 (7), pp.075111. ⟨10.1103/PhysRevB.99.075111⟩. ⟨hal-03171537⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Integrability and duality in spin chains – Archive ouverte HAL

### Eyzo StoutenPieter W. ClaeysJean-Sébastien CauxVladimir Gritsev

^{1}*Phys.Rev.B*, 2019, 99 (7), pp.075111. ⟨10.1103/PhysRevB.99.075111⟩. ⟨hal-03171537⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Integrability and duality in spin chains – Archive ouverte HAL

### Eyzo StoutenPieter W. ClaeysJean-Sébastien CauxVladimir Gritsev

^{1}*Phys.Rev.B*, 2019, 99 (7), pp.075111. ⟨10.1103/PhysRevB.99.075111⟩. ⟨hal-03171537⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Receptor crosstalk improves concentration sensing of multiple ligands – Archive ouverte HAL

### Martín Carballo-PachecoJonathan Desponds

^{1}Tatyana GavrilchenkoAndreas MayerRoshan PrizakGautam ReddyIlya NemenmanThierry Mora^{2, 3}#### Martín Carballo-Pacheco, Jonathan Desponds, Tatyana Gavrilchenko, Andreas Mayer, Roshan Prizak, et al.. Receptor crosstalk improves concentration sensing of multiple ligands.

*Physical Review E*, American Physical Society (APS), 2019, 99 (2), ⟨10.1103/PhysRevE.99.022423⟩. ⟨hal-02569923⟩- 1. PCC - Physico-Chimie-Curie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Physique Statistique et Inférence pour la Biologie

## Multi-Fluid Hydrodynamics in Charge Density Waves with Collective, Electronic, and Solitonic Densities and Currents – Archive ouverte HAL

### S. Brazovskii

^{1}N. Kirova^{2}#### S. Brazovskii, N. Kirova. Multi-Fluid Hydrodynamics in Charge Density Waves with Collective, Electronic, and Solitonic Densities and Currents.

*Journal of Experimental and Theoretical Physics (JETP) / Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki*, MAIK Nauka/Interperiodica, 2019, 129 (4), pp.659-668. ⟨10.1134/S1063776119100017⟩. ⟨hal-02512280⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Modeling the Correlated Activity of Neural Populations: A Review – Archive ouverte HAL

### Christophe Gardella

^{1}Olivier Marre^{1}Thierry Mora^{2, 3}#### Christophe Gardella, Olivier Marre, Thierry Mora. Modeling the Correlated Activity of Neural Populations: A Review.

*Neural Computation*, Massachusetts Institute of Technology Press (MIT Press), 2019, 31 (2), pp.233-269. ⟨10.1162/neco_a_01154⟩. ⟨hal-02569955⟩- 1. Institut de la Vision
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Physique Statistique et Inférence pour la Biologie

## Mechanical properties of lipid bilayers: a note on the Poisson ratio – Archive ouverte HAL

### M. Mert Terzi

^{1}Markus Deserno^{2}John Nagle^{3}#### M. Mert Terzi, Markus Deserno, John Nagle. Mechanical properties of lipid bilayers: a note on the Poisson ratio.

*Soft Matter*, Royal Society of Chemistry, 2019, 15 (44), pp.9085-9092. ⟨10.1039/c9sm01290g⟩. ⟨hal-02512307⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CMU - Carnegie Mellon University [Pittsburgh]
- 3. University of Ulster

## Long-time position distribution of an active Brownian particle in two dimensions – Archive ouverte HAL

### Urna Basu

^{1}Satya N. Majumdar^{2}Alberto Rosso^{2}Satya Majumdar^{2}Gregory Schehr^{2}#### Urna Basu, Satya N. Majumdar, Alberto Rosso, Satya Majumdar, Gregory Schehr. Long-time position distribution of an active Brownian particle in two dimensions.

*Physical Review E*, American Physical Society (APS), 2019, 100 (6), ⟨10.1103/PhysRevE.100.062116⟩. ⟨hal-02512255⟩We study the late time dynamics of a single active Brownian particle in two dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that at late times $t\gg D_R^{-1}$, while the position probability distribution $P(x,y,t)$ in the $x$-$y$ plane approaches a Gaussian form near its peak describing the typical diffusive fluctuations, it has non-Gaussian tails describing atypical rare fluctuations when $\sqrt{x^2+y^2}\sim v_0 t$. In this regime, the distribution admits a large deviation form, $P(x,y,t) \sim \exp\left[-t\, D_R\, \Phi\left(\sqrt{x^2+y^2}/(v_0 t)\right)\right]$, where we compute the rate function $\Phi(z)$ analytically and also numerically using an importance sampling method. We show that the rate function $\Phi(z)$, encoding the rare fluctuations, still carries the trace of activity even at late times. Another way of detecting activity at late times is to subject the active particle to an external harmonic potential. In this case we show that the stationary distribution $P_\text{stat}(x,y)$ depends explicitly on the activity parameter $D_R^{-1}$ and undergoes a crossover, as $D_R$ increases, from a ring shape in the strongly active limit ($D_R\to 0$) to a Gaussian shape in the strongly passive limit $(D_R\to \infty)$.

- 1. Theoretical Condensed Matter Physics Division
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Integrability and duality in spin chains – Archive ouverte HAL

### Eyzo StoutenPieter W. ClaeysJean-Sébastien CauxVladimir Gritsev

^{1}*Phys.Rev.B*, 2019, 99 (7), pp.075111. ⟨10.1103/PhysRevB.99.075111⟩. ⟨hal-03171537⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## How many different clonotypes do immune repertoires contain? – Archive ouverte HAL

### Thierry Mora

^{1, 2}Aleksandra Walczak^{2}#### Thierry Mora, Aleksandra Walczak. How many different clonotypes do immune repertoires contain?.

*Current Opinion in Systems Biology*, Elsevier, 2019, 18, pp.104-110. ⟨10.1016/j.coisb.2019.10.001⟩. ⟨hal-02569976⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Physique Statistique et Inférence pour la Biologie

## Fault Heterogeneity and the Connection between Aftershocks and Afterslip – Archive ouverte HAL

### Eugenio Lippiello

^{1}Giuseppe Petrillo^{1}François Landes^{2, 3, 4}Alberto Rosso^{5}#### Eugenio Lippiello, Giuseppe Petrillo, François Landes, Alberto Rosso. Fault Heterogeneity and the Connection between Aftershocks and Afterslip.

*Bulletin of the Seismological Society of America*, Seismological Society of America, 2019, 109 (3), pp.1156-1163. ⟨10.1785/0120180244⟩. ⟨hal-02156407⟩Whether aftershocks originate directly from the mainshock and surrounding stress environment or from afterslip dynamics is crucial to the understanding of the nature of aftershocks. We build on a classical description of the fault and creeping regions as two blocks connected elastically, subject to different friction laws. We show analytically that, upon introduction of variability in the fault plane’s static friction threshold, a non trivial stick-slip dynamics ensues. In particular we support the hypothesis that the aftershock occurrence rate is proportional to the afterslip rate, up to a corrective factor that is also computed. Thus, the Omori law originates from the afterslip’s logarithmic evolution in the velocity-strengthening region. We confirm these analytical results with numerical simulations, generating synthetic catalogs with statistical features in good agreement with instrumental catalogs. In particular we recover the Gutenberg-Richter law with a realistic b-value (b'1) when Coulomb stress thresholds obey a power law distribution.

- 1. Department of Mathematics and Physics [Caserta]
- 2. LRI - Laboratoire de Recherche en Informatique
- 3. TAU - TAckling the Underspecified
- 4. UP11 UFR Sciences - Université Paris-Sud 11 - Faculté des Sciences
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Comparing dynamics: deep neural networks versus glassy systems – Archive ouverte HAL

### Marco Baity-Jesi

^{1}Levent Sagun^{2}Mario Geiger^{3}Stefano Spigler^{4}Gérard Ben Arous^{5}Chiara Cammarota^{6}Yann Lecun^{7}Matthieu Wyart^{3}Giulio Biroli^{8, 9, 10}#### Marco Baity-Jesi, Levent Sagun, Mario Geiger, Stefano Spigler, Gérard Ben Arous, et al.. Comparing dynamics: deep neural networks versus glassy systems.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (12), pp.124013. ⟨10.1088/1742-5468/ab3281⟩. ⟨hal-02569114⟩- 1. Department of Physics and Astronomy [Philadelphia]
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 3. EPFL - Ecole Polytechnique Fédérale de Lausanne
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. IMA - Institut de Mathématiques
- 6. King‘s College London
- 7. FAIR - Facebook AI Research [Paris]
- 8. SPhT - Service de Physique Théorique
- 9. LPS - Laboratoire de Physique Statistique de l'ENS
- 10. Systèmes Désordonnés et Applications

## Archive ouverte HAL – When Random Walkers Help Solving Intriguing Integrals

### Satya Majumdar

^{1}Emmanuel Trizac^{1}#### Satya Majumdar, Emmanuel Trizac. When Random Walkers Help Solving Intriguing Integrals.

*Physical Review Letters*, American Physical Society, 2019, 123 (2), ⟨10.1103/PhysRevLett.123.020201⟩. ⟨hal-02291790⟩We revisit a family of integrals that delude intuition, and that recently appeared in mathematical literature in connection with computer algebra package verification. We show that the remarkable properties displayed by these integrals become transparent when formulated in the language of random walks. In turn, the random walk view naturally leads to a plethora of nontrivial generalizations, that are worked out. Related complex identities are also derived, without the need of explicit calculation. The crux of our treatment lies in a causality argument where a message that travels at finite speed signals the existence of a boundary.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material

### M. Isoard

^{1}A. M. Kamchatnov^{2}N. Pavloff^{1}#### M. Isoard, A. M. Kamchatnov, N. Pavloff. Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material.

*Physical Review A*, American Physical Society 2019, 99 (5), ⟨10.1103/PhysRevA.99.053819⟩. ⟨hal-02291908⟩We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described within a nondispersive approximation by means of Riemann's approach. For larger distances, wave breaking occurs, leading to the formation of dispersive shocks at both ends of the pulse. We describe this phenomenon within Whitham modulation theory, which yields an excellent agreement with numerical simulations. Our analytic approach makes it possible to extract the leading asymptotic behavior of the parameters of the shock.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute of Spectroscopy

## Archive ouverte HAL – Two faces of Douglas-Kazakov transition: from Yang-Mills theory to random walks and beyond

### Alexander GorskyAlexey MilekhinSergei Nechaev

^{1}#### Alexander Gorsky, Alexey Milekhin, Sergei Nechaev. Two faces of Douglas-Kazakov transition: from Yang-Mills theory to random walks and beyond.

*Nuclear Physics B*, Elsevier, 2019. ⟨hal-02365447⟩Being inspired by the connection between 2D Yang-Mills (YM) theory and (1+1)D "vicious walks" (VW), we consider different incarnations of large-$N$ Douglas-Kazakov (DK) phase transition in gauge field theories and stochastic processes focusing at possible physical interpretations. We generalize the connection between YM and VW, study the influence of initial and final distributions of walkers on the DK phase transition, and describe the effect of the $\theta$-term in corresponding stochastic processes. We consider the Jack stochastic process involving Calogero-type interaction between walkers and investigate the dependence of DK transition point on a coupling constant. Relying on the relation between large-$N$ 2D $q$-YM and extremal black hole (BH) with large-$N$ magnetic charge, we speculate about a physical interpretation of a DK phase transitions in a 4D extremal charged BH.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Tunable corrugated patterns in an active nematic sheet

### Anis Senoussi

^{1}Shunnichi Kashida^{1}Raphaël Voituriez^{2}Jean-Christophe Galas^{1}Ananyo Maitra^{3}André Estévez-Torres^{1}#### Anis Senoussi, Shunnichi Kashida, Raphaël Voituriez, Jean-Christophe Galas, Ananyo Maitra, et al.. Tunable corrugated patterns in an active nematic sheet.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2019, pp.201912223. ⟨10.1073/pnas.1912223116⟩. ⟨hal-02334253⟩- 1. LJP - Laboratoire Jean Perrin
- 2. LJP - Laboratoire Jean Perrin
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Topological proximity effects in a Haldane graphene bilayer system

### Peng Cheng

^{1}Philipp W. KleinKirill Plekhanov^{2, 3}Klaus Sengstock^{4}Monika AidelsburgerChristof Weitenberg^{5}Karyn Le Hur^{2}Philipp KleinKaryn Le Hur^{2}#### Peng Cheng, Philipp W. Klein, Kirill Plekhanov, Klaus Sengstock, Monika Aidelsburger, et al.. Topological proximity effects in a Haldane graphene bilayer system.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 100 (8), ⟨10.1103/PhysRevB.100.081107⟩. ⟨hal-02291915⟩We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. We propose an alternative definition of the topological invariant on the Bloch sphere.

- 1. DALEMBERT - Institut Jean Le Rond d'Alembert
- 2. CPHT - Centre de Physique Théorique [Palaiseau]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Zentrum für Optische Quantentechnologien
- 5. MPQ - Max-Planck-Institut für Quantenoptik

## Archive ouverte HAL – Time Between the Maximum and the Minimum of a Stochastic Process

### Francesco Mori

^{1}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Time Between the Maximum and the Minimum of a Stochastic Process.

*Physical Review Letters*, American Physical Society, 2019, 123 (20), ⟨10.1103/PhysRevLett.123.200201⟩. ⟨hal-02395492⟩We present an exact solution for the probability density function $P(\tau=t_{\min}-t_{\max}|T)$ of the time-difference between the minimum and the maximum of a one-dimensional Brownian motion of duration $T$. We then generalise our results to a Brownian bridge, i.e. a periodic Brownian motion of period $T$. We demonstrate that these results can be directly applied to study the position-difference between the minimal and the maximal height of a fluctuating $(1+1)$-dimensional Kardar-Parisi-Zhang interface on a substrate of size $L$, in its stationary state. We show that the Brownian motion result is universal and, asymptotically, holds for any discrete-time random walk with a finite jump variance. We also compute this distribution numerically for L\'evy flights and find that it differs from the Brownian motion result.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Three-body interaction near a narrow two-body zero crossing

### A. Pricoupenko

^{1}D. S. Petrov^{1}#### A. Pricoupenko, D. S. Petrov. Three-body interaction near a narrow two-body zero crossing.

*Physical Review A*, American Physical Society 2019, 100 (4), ⟨10.1103/PhysRevA.100.042707⟩. ⟨hal-02395504⟩We calculate the effective three-body force for bosons interacting with each other by a two-body potential tuned to a narrow zero crossing in any dimension. We use the standard two-channel model parametrized by the background atom-atom interaction strength, the amplitude of the open-channel to closed-channel coupling, and the atom-dimer interaction strength. The three-body force originates from the atom-dimer interaction, but it can be dramatically enhanced for narrow crossings, i.e., for small atom-dimer conversion amplitudes. This effect can be used to stabilize quasi-two-dimensional dipolar atoms and molecules.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The equilibrium landscape of the Heisenberg spin chain

### Enej IlievskiEoin Quinn

^{1}#### Enej Ilievski, Eoin Quinn. The equilibrium landscape of the Heisenberg spin chain.

*SciPost Physics*, SciPost Foundation, 2019, 7 (3), ⟨10.21468/SciPostPhys.7.3.033⟩. ⟨hal-02295879⟩We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical Y-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The algebraic area of closed lattice random walks

### Stephane Ouvry

^{1}Shuang Wu^{1}#### Stephane Ouvry, Shuang Wu. The algebraic area of closed lattice random walks.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, ⟨10.04098⟩. ⟨hal-02292208⟩We propose a formula for the enumeration of closed lattice random walks of length $n$ enclosing a given algebraic area. The information is contained in the Kreft coefficients which encode, in the commensurate case, the Hofstadter secular equation for a quantum particle hopping on a lattice coupled to a perpendicular magnetic field. The algebraic area enumeration is possible because it is split in $2^{n/2-1}$ pieces, each tractable in terms of explicit combinatorial expressions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Stress-dependent amplification of active forces in nonlinear elastic media

### Pierre Ronceray

^{1}Chase Broedersz^{2}Martin Lenz^{3}*Soft Matter*, Royal Society of Chemistry, 2019The production of mechanical stresses in living organisms largely relies on localized, force-generating active units embedded in filamentous matrices. Numerical simulations of discrete fiber networks with fixed boundaries have shown that buckling in the matrix dramatically amplifies the resulting active stresses. Here we extend this result to a bucklable continuum elastic medium subjected to an arbitrary external stress, and derive analytical expressions for the active, nonlinear constitutive relations characterizing the full active medium. Inserting these relations into popular "active gel" descriptions of living tissues and the cytoskeleton will enable investigations into nonlinear regimes previously inaccessible due to the phenomenological nature of these theories.

- 1. Princeton University
- 2. Arnold Sommerfeld Center for Theoretical Physics
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Statistical mechanics of asymmetric tethered membranes: Spiral and crumpled phases

### Tirthankar Banerjee

^{1}Niladri Sarkar^{2}John Toner^{2}Abhik Basu#### Tirthankar Banerjee, Niladri Sarkar, John Toner, Abhik Basu. Statistical mechanics of asymmetric tethered membranes: Spiral and crumpled phases.

*Physical Review E*, American Physical Society (APS), 2019, 99 (5), ⟨10.1103/PhysRevE.99.053004⟩. ⟨hal-02291841⟩We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends upon the local in-plane dilation of the tethered network. This in turn leads to long-ranged interactions between the local mean and Gaussian curvatures, which is not present in symmetric tethered membranes. This interplay between asymmetry and Gaussian curvature leads to a new {\em double-spiral} phase not found in symmetric tethered membranes. At temperature $T=0$, tethered membranes of arbitrarily large size are always rolled up tightly into a conjoined pair of Archimedes' spirals. At finite $T$ this spiral structure swells up significantly into algebraic spirals characterized by universal exponents which we calculate. These spirals have long range orientational order, and are the asymmetric analogs of statistically flat symmetric tethered membranes. We also find that sufficiently strong asymmetry can trigger a structural instability leading to crumpling of these membranes as well. This provides a new route to crumpling for asymmetric tethered membranes. We calculate the maximum linear extent $L_c$ beyond which the membrane crumples, and calculate the universal dependence of $L_c$ on the membrane parameters. By tuning the asymmetry parameter, $L_c$ can be continuously varied, implying a {\em scale-dependent} crumpling. Our theory can be tested on controlled experiments on lipids with artificial deposits of spectrin filaments, in-vitro experiments on %\sout{artificial deposition of spectrin filaments on} red blood cell membrane extracts, %\sout{after %depletion of adenosine-tri-phosphate molecules} and on graphene coated on one side.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. MPI-PKS - Max Planck Institute for the Physics of Complex Systems

## Archive ouverte HAL – Spontaneous rotation can stabilise ordered chiral active fluids

### Ananyo Maitra

^{1}Martin Lenz^{1}#### Ananyo Maitra, Martin Lenz. Spontaneous rotation can stabilise ordered chiral active fluids.

*Nature Communications*, Nature Publishing Group, 2019, 10 (1), ⟨10.1038/s41467-019-08914-7⟩. ⟨hal-02102862⟩Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases are by now well established, the effect of chirality on these phases is much less studied. In this paper, we present the first complete dynamical theory of orientationally ordered chiral particles in two-dimensional incompressible systems. We show that phase-coherent states of rotating chiral particles are remarkably stable in both momentum-conserved and non-conserved systems in contrast to their non-rotating counterparts. Furthermore, defect separation -- which drives chaotic flows in non-rotating active fluids -- is suppressed by intrinsic rotation of chiral active particles. We thus establish chirality as a source of dramatic stabilization in active systems, which could be key in interpreting the collective behaviours of some biological tissues, cytoskeletal systems and collections of bacteria.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Smoluchowski flux and lamb-lion problems for random walks and Lévy flights with a constant drift

### Satya Majumdar

^{1}Philippe Mounaix^{2}Gregory Schehr^{1}#### Satya Majumdar, Philippe Mounaix, Gregory Schehr. Smoluchowski flux and lamb-lion problems for random walks and Lévy flights with a constant drift.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (8), pp.083214. ⟨10.1088/1742-5468/ab35e5⟩. ⟨hal-02272076⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CPHT - Centre de Physique Théorique [Palaiseau]

## Archive ouverte HAL – Simply modified GKL density classifiers that reach consensus faster

### J. Ricardo G. Mendonça

^{1}#### J. Ricardo G. Mendonça. Simply modified GKL density classifiers that reach consensus faster.

*Modern Physics Letters A*, World Scientific Publishing, 2019, 383 (19), pp.2264-2266. ⟨10.1016/j.physleta.2019.04.033⟩. ⟨hal-02291810⟩The two-state Gacs-Kurdyumov-Levin (GKL) cellular automaton has been a staple model in the study of complex systems due to its ability to classify binary arrays of symbols according to their initial density. We show that a class of modified GKL models over extended neighborhoods, but still involving only three cells at a time, achieves comparable density classification performance but in some cases reach consensus more than twice as fast. Our results suggest the time to consensus (relative to the length of the CA) as a complementary measure of density classification performance.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Shortcut to stationary regimes: A simple experimental demonstration

### Stéphane Faure

^{1}Sergio Ciliberto^{2}Emmanuel Trizac^{3}David Guéry-Odelin^{1}*American Journal of Physics*, American Association of Physics Teachers, 2019, 87 (2), pp.125-129. 〈10.1119/1.5082933〉- 1. Atomes Froids (LCAR)
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks

### Jonathan Bares

^{1}Daniel Bonamy^{2}Alberto Rosso^{3}#### Jonathan Bares, Daniel Bonamy, Alberto Rosso. Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks.

*Physical Review E*, American Physical Society (APS), 2019, 100 (2), pp.023001. ⟨10.1103/PhysRevE.100.023001⟩. ⟨hal-02269109⟩Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.

- 1. Servex - Moyens expérimentaux
- 2. SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Run-and-tumble particle in one-dimensional confining potentials: Steady-state, relaxation, and first-passage properties

### Abhishek Dhar

^{1}Anupam Kundu^{1}Satya N. Majumdar^{2}Sanjib Sabhapandit^{3}Gregory Schehr^{2}#### Abhishek Dhar, Anupam Kundu, Satya N. Majumdar, Sanjib Sabhapandit, Gregory Schehr. Run-and-tumble particle in one-dimensional confining potentials: Steady-state, relaxation, and first-passage properties.

*Physical Review E*, American Physical Society (APS), 2019, 99 (3), ⟨10.1103/PhysRevE.99.032132⟩. ⟨hal-02102138⟩We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x) = \alpha \, |x|^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$ values. We show that the stationary probability density $P(x)$ has a rich behavior in the $(p, \alpha)$-plane. For $p>1$, the distribution has a finite support in $[x_-,x_+]$ and there is a critical line $\alpha_c(p)$ that separates an active-like phase for $\alpha > \alpha_c(p)$ where $P(x)$ diverges at $x_\pm$, from a passive-like phase for $\alpha < \alpha_c(p)$ where $P(x)$ vanishes at $x_\pm$. For $p<1$, the stationary density $P(x)$ collapses to a delta function at the origin, $P(x) = \delta(x)$. In the marginal case $p=1$, we show that, for $\alpha < \alpha_c$, the stationary density $P(x)$ is a symmetric exponential, while for $\alpha > \alpha_c$, it again is a delta function $P(x) = \delta(x)$. For the special cases $p=2$ and $p=1$, we obtain exactly the full time-dependent distribution $P(x,t)$, that allows us to study how the system relaxes to its stationary state. In addition, in these two cases, we also study analytically the full distribution of the first-passage time to the origin. Numerical simulations are in complete agreement with our analytical predictions.

- 1. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Raman Research Insitute

## Archive ouverte HAL – Rotating trapped fermions in two dimensions and the complex Ginibre ensemble: Exact results for the entanglement entropy and number variance

### Bertrand Lacroix-A-Chez-Toine

^{1}Satya N. Majumdar^{1}Grégory Schehr^{1}*Phys.Rev.A*, 2019, 99 (2), pp.021602. 〈10.1103/PhysRevA.99.021602〉We establish an exact mapping between the positions of N noninteracting fermions in a two-dimensional rotating harmonic trap in its ground state and the eigenvalues of the N×N complex Ginibre ensemble of random matrix theory (RMT). Using RMT techniques, we make precise predictions for the statistics of the positions of the fermions, both in the bulk as well as at the edge of the trapped Fermi gas. In addition, we compute exactly, for any finite N, the Rényi entanglement entropy and the number variance of a disk of radius r in the ground state. We show that while these two quantities are proportional to each other in the (extended) bulk, this is no longer the case very close to the trap center nor at the edge. Near the edge, and for large N, we provide exact expressions for the scaling functions associated with these two observables.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Rolled Up or Crumpled: Phases of Asymmetric Tethered Membranes

### Tirthankar Banerjee

^{1}Niladri Sarkar^{2}John Toner^{2}Abhik Basu#### Tirthankar Banerjee, Niladri Sarkar, John Toner, Abhik Basu. Rolled Up or Crumpled: Phases of Asymmetric Tethered Membranes.

*Physical Review Letters*, American Physical Society, 2019, 122 (21), ⟨10.1103/PhysRevLett.122.218002⟩. ⟨hal-02291826⟩We show that inversion-asymmetric tethered membranes exhibit a new double-spiral phase with long range orientational order not present in symmetric membranes. We calculate the universal algebraic spiral shapes of these membranes in this phase. Asymmetry can trigger the crumpling of these membranes as well. In-vitro experiments on lipid, red blood cell membrane extracts, and on graphene coated on one side, could test these predictions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. MPI-PKS - Max Planck Institute for the Physics of Complex Systems

## Archive ouverte HAL – Role of information backflow in the emergence of quantum Darwinism

### Nadia Milazzo

^{1}Salvatore LorenzoMauro Paternostro^{2}G. Massimo Palma#### Nadia Milazzo, Salvatore Lorenzo, Mauro Paternostro, G. Massimo Palma. Role of information backflow in the emergence of quantum Darwinism.

*Physical Review A*, American Physical Society 2019, 100 (1), ⟨10.1103/PhysRevA.100.012101⟩. ⟨hal-02291799⟩Quantum Darwinism attempts to explain the emergence of objective reality of the state of a quantum system in terms of redundant information about the system acquired by independent non interacting fragments of the environment. The consideration of interacting environmental elements gives rise to a rich phenomenology, including the occurrence of non-Markovian features, whose effects on objectification {\it a' la} quantum Darwinism needs to be fully understood. We study a model of local interaction between a simple quantum system and a multi-mode environment that allows for a clear investigation of the interplay between information trapping and propagation in the environment and the emergence of quantum Darwinism. We provide strong evidence of the correlation between non-Markovianity and quantum Darwinism in such a model, thus providing strong evidence of a potential link between such fundamental phenomena.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centre for Theoretical Atomic, Molecular and Optical Physics

## Archive ouverte HAL – Rigid Fuchsian systems in 2-dimensional conformal field theories

### Vladimir BelavinYoshishige HaraokaRaoul Santachiara

^{1}*Commun.Math.Phys.*, 2019, 365 (1), pp.17-60. 〈10.1007/s00220-018-3274-x〉We investigate Fuchsian equations arising in the context of 2-dimensional conformal field theory (CFT) and we apply the Katz theory of Fucshian rigid systems to solve some of these equations. We show that the Katz theory provides a precise mathematical framework to answer the question whether the fusion rules of degenerate primary fields are enough for determining the differential equations satisfied by their correlation functions. We focus on the case of ${\mathcal{W}_{3}}$ Toda CFT: we argue that the differential equations arising for four-point conformal blocks with one nth level semi-degenerate field and a fully-degenerate one in the fundamental sl$_{3}$ representation are associated to Fuchsian rigid systems. We show how to apply Katz theory to determine the explicit form of the differential equations, the integral expression of solutions and the monodromy group representation. The theory of twisted homology is also used in the analysis of the integral expression. The computation of the connection coefficients is done for the first time in the case of a Katz system with multiplicities, thus extending the work done by Oshima in the multiplicity free case. This approach allows us to construct the corresponding fusion matrices and to perform the whole bootstrap program: new explicit factorization of ${\mathcal{W}_{3}}$ correlation functions as well as shift relations between structure constants for general Toda theories are also provided.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Receptor crosstalk improves concentration sensing of multiple ligands

### Martín Carballo-PachecoJonathan Desponds

^{1}Tatyana GavrilchenkoAndreas MayerRoshan PrizakGautam ReddyIlya NemenmanThierry Mora^{2, 3}#### Martín Carballo-Pacheco, Jonathan Desponds, Tatyana Gavrilchenko, Andreas Mayer, Roshan Prizak, et al.. Receptor crosstalk improves concentration sensing of multiple ligands.

*Physical Review E*, American Physical Society (APS), 2019, 99 (2), ⟨10.1103/PhysRevE.99.022423⟩. ⟨hal-02569923⟩- 1. PCC - Physico-Chimie-Curie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Physique Statistique et Inférence pour la Biologie

## Archive ouverte HAL – Quantum Hall skyrmions at ν = 0 , ± 1 in monolayer graphene

### Thierry Jolicoeur

^{1}Bradraj Pandey^{1}#### Thierry Jolicoeur, Bradraj Pandey. Quantum Hall skyrmions at ν = 0 , ± 1 in monolayer graphene.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 100 (11), ⟨10.1103/PhysRevB.100.115422⟩. ⟨hal-02291775⟩Monolayer graphene under a strong perpendicular field exhibit quantum Hall ferromagnetism with spontaneously broken spin and valley symmetry. The approximate SU(4) spin/valley symmetry is broken by small lattice scale effects in the central Landau level corresponding to filling factors $\nu=0,\pm 1$. Notably the ground state at $\nu=0$ is believed to be a canted antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component of the magnetic field parallel to the layer and the strength of small anisotropies. We study the skyrmions for the filling factors $\nu=\pm 1,0$ by using exact diagonalizations on the spherical geometry. If we neglect anisotropies we confirm the validity of the standard skyrmion picture generalized to four degrees of freedom. For filling factor $\nu=- 1$ the hole skyrmion is an infinite-size valley skyrmion with full spin polarization because it does not feel the anisotropies. The electron skyrmion is also always of infinite size. In the F phase it is always fully polarized while in the AF phase it undergoes continuous magnetization under increasing Zeeman energy. In the case of $\nu=0$ the skyrmion is always maximally localized in space both in F and AF phase. In the F phase it is fully polarized while in the AF it has also progressive magnetization with Zeeman energy. The magnetization process is unrelated to the spatial profile of the skyrmions contrary to the SU(2) case. In all cases the skyrmion physics is dominated by the competition between anisotropies and Zeeman effect but not directly by the Coulomb interactions, breaking universal scaling with the ratio Zeeman to Coulomb energy.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Quadratic Mean Field Games

### Denis Ullmo

^{1}Igor Swiecicki^{2, 1}Thierry Gobron^{2}#### Denis Ullmo, Igor Swiecicki, Thierry Gobron. Quadratic Mean Field Games.

*Physics Reports*, Elsevier, 2019. ⟨hal-02291869⟩Mean field games were introduced independently by J-M. Lasry and P-L. Lions, and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new approach to optimization problems with a large number of interacting agents. The description of such models split in two parts, one describing the evolution of the density of players in some parameter space, the other the value of a cost functional each player tries to minimize for himself, anticipating on the rational behavior of the others. Quadratic Mean Field Games form a particular class among these systems, in which the dynamics of each player is governed by a controlled Langevin equation with an associated cost functional quadratic in the control parameter. In such cases, there exists a deep relationship with the non-linear Schr\"odinger equation in imaginary time, connexion which lead to effective approximation schemes as well as a better understanding of the behavior of Mean Field Games. The aim of this paper is to serve as an introduction to Quadratic Mean Field Games and their connexion with the non-linear Schr\"odinger equation, providing to physicists a good entry point into this new and exciting field.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTM - Laboratoire de Physique Théorique et Modélisation

## Archive ouverte HAL – Properties of additive functionals of Brownian motion with resetting

### Frank Den Hollander

^{1}Satya N. Majumdar^{2}Janusz M. Meylahn^{1}Hugo Touchette^{3}#### Frank Den Hollander, Satya N. Majumdar, Janusz M. Meylahn, Hugo Touchette. Properties of additive functionals of Brownian motion with resetting.

*Journal of Physics A: Mathematical and General*, IOP Publishing, 2019. ⟨hal-02102127⟩We study the distribution of additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate and placed back to a given reset position. Our goal is two-fold: (1) For general functionals, we derive a large deviation principle in the presence of resetting and identify the large deviation rate function in terms of a variational formula involving large deviation rate functions without resetting. (2) For three examples of functionals (positive occupation time, area and absolute area), we investigate the effect of resetting by computing distributions and moments, using a formula that links the generating function with resetting to the generating function without resetting.

- 1. Leiden University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institute of Theoretical Physics

## Archive ouverte HAL – Poincaré invariance in NRQCD and potential NRQCD revisited

### Matthias BerweinNora Brambilla

^{1}Sungmin Hwang^{2}Antonio Vairo^{1}#### Matthias Berwein, Nora Brambilla, Sungmin Hwang, Antonio Vairo. Poincaré invariance in NRQCD and potential NRQCD revisited.

*Physical Review D*, American Physical Society, 2019, 99 (9), ⟨10.1103/PhysRevD.99.094008⟩. ⟨hal-02292167⟩We investigate how fields transform under the Poincar\'e group in nonrelativistic effective field theories of QCD. In constructing these transformations, we rely only on symmetries and field redefinitions to limit the number of allowed terms. By requiring invariance of the action under these transformations, nontrivial relations between Wilson coefficients for both nonrelativistic QCD and potential nonrelativistic QCD are derived. We show explicitly how the Poincar\'e algebra is satisfied, and how this gives complementary information on the Wilson coefficients. We also briefly discuss the implications of our results, as well as the possibility of applying this method to other types of effective field theories.

- 1. Physik Department [Garching]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Phase transitions and pattern formation in ensembles of phase-amplitude solitons in quasi-one-dimensional electronic systems

### P. Karpov

^{1}S. Brazovskii^{2}*Physical Review E*, American Physical Society (APS), 2019, 99 (2), 〈10.1103/PhysRevE.99.022114〉Most common types of symmetry breaking in quasi-one-dimensional electronic systems possess a combined manifold of states degenerate with respect to both the phase $\theta$ and the amplitude $A$ sign of the order parameter $A\exp(i\theta)$. These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge densities. To understand statistical properties and the phase diagram in the course of cooling under the controlled parameters, we present here an analytical treatment supported by Monte Carlo simulations for a generic coarse-grained two-fields model of XY-Ising type. The degeneracies give rise to two coexisting types of topologically nontrivial configurations: phase vortices and amplitude kinks -- the solitons. In 2D, 3D states with long-range (or BKT type) orders, the topological confinement sets in at a temperature $T=T_1$ which binds together the kinks and unusual half-integer vortices. At a lower $T=T_2$, the solitons start to aggregate into walls formed as rods of amplitude kinks which are ultimately terminated by half-integer vortices. With lowering $T$, the walls multiply passing sequentially across the sample. The presented results indicate a possible physical realization of a peculiar system of half-integer vortices with rods of amplitude kinks connecting their cores. Its experimental realization becomes feasible in view of recent successes in real space observations and even manipulations of domain walls in correlated electronic systems.

- 1. MISIS - National University of Science and Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain

### Elisabeth Agoritsas

^{1}Thibaud Maimbourg^{2}Francesco Zamponi^{3}#### Elisabeth Agoritsas, Thibaud Maimbourg, Francesco Zamponi. Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (33), pp.334001. ⟨10.1088/1751-8121/ab2b68⟩. ⟨hal-02291782⟩As an extension of the isotropic setting presented in the companion paper [J. Phys. A 52, 144002 (2019)], we consider the Langevin dynamics of a many-body system of pairwise interacting particles in $d$ dimensions, submitted to an external shear strain. We show that the anisotropy introduced by the shear strain can be simply addressed by moving into the co-shearing frame, leading to simple dynamical mean field equations in the limit ${d\to\infty}$. The dynamics is then controlled by a single one-dimensional effective stochastic process which depends on three distinct strain-dependent kernels - self-consistently determined by the process itself - encoding the effective restoring force, friction and noise terms due to the particle interactions. From there one can compute dynamical observables such as particle mean-square displacements and shear stress fluctuations, and eventually aim at providing an exact ${d \to \infty}$ benchmark for liquid and glass rheology. As an application of our results, we derive dynamically the 'state-following' equations that describe the static response of a glass to a finite shear strain until it yields.

- 1. EPFL - Ecole Polytechnique Fédérale de Lausanne
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LPENS - UMR 8023 - Laboratoire de physique de l'ENS - ENS Paris

## Archive ouverte HAL – Optimal work in a harmonic trap with bounded stiffness

### Carlos A. Plata

^{1, 2}David Guéry-Odelin^{3}E. Trizac^{4}A. Prados^{1}*Physical Review E*, American Physical Society (APS), 2019, 99 (1), pp.012140. 〈10.1103/PhysRevE.99.012140〉We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness $\kappa$. We work out the optimal time dependence $\kappa(t)$ by minimising the work performed on the particle under the non-holonomic constraint $0\leq\kappa\leq\kappa_{\max}$, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analysed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time $t_{\text{f}}$ and the desired compression ratio $\kappa_{\text{f}}/\kappa_{\text{\i}}$, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimisation of heat engines.

- 1. Universidad de Sevilla
- 2. Dipartimento di Fisica e Astronomia "Galileo Galilei"
- 3. Atomes Froids (LCAR)
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Optimal measurement strategies for fast entanglement detection

### N. Milazzo

^{1}D. BraunO. Giraud^{1}#### N. Milazzo, D. Braun, O. Giraud. Optimal measurement strategies for fast entanglement detection.

*Physical Review A*, American Physical Society 2019, 100 (1), ⟨10.1103/PhysRevA.100.012328⟩. ⟨hal-02291898⟩With the advance of quantum information technology, the question of how to most efficiently test quantum circuits is becoming of increasing relevance. Here we introduce the statistics of lengths of measurement sequences that allows one to certify entanglement across a given bi-partition of a multi-qubit system over the possible sequence of measurements of random unknown states, and identify the best measurement strategies in the sense of the (on average) shortest measurement sequence of (multi-qubit) Pauli measurements. The approach is based on the algorithm of truncated moment sequences that allows one to deal naturally with incomplete information, i.e. information that does not fully specify the quantum state. We find that the set of measurements corresponding to diagonal matrix elements of the moment matrix of the state are particularly efficient. For symmetric states their number grows only like the third power of the number $N$ of qubits. Their efficiency grows rapidly with $N$, leaving already for $N=4$ less than a fraction $10^{-6}$ of randomly chosen entangled states undetected.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction

### D. V. Kurlov

^{1}S. I. Matveenko^{2}V. Gritsev^{3}G. V. Shlyapnikov^{2}#### D. V. Kurlov, S. I. Matveenko, V. Gritsev, G. V. Shlyapnikov. One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction.

*Physical Review A*, American Physical Society 2019, 99 (4), ⟨10.1103/PhysRevA.99.043631⟩. ⟨hal-02291881⟩We consider a one-dimensional (1D) two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.

- 1. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Physics Department

## Archive ouverte HAL – One-Dimensional Quasicrystals with Power-Law Hopping

### X. DengS. RayS. Sinha

^{1}G. v. Shlyapnikov^{2}L. Santos#### X. Deng, S. Ray, S. Sinha, G. v. Shlyapnikov, L. Santos. One-Dimensional Quasicrystals with Power-Law Hopping.

*Physical Review Letters*, American Physical Society, 2019, 123 (2), ⟨10.1103/PhysRevLett.123.025301⟩. ⟨hal-02291885⟩One-dimensional quasi-periodic systems with power-law hopping, $1/r^a$, differ from both the standard Aubry-Azbel-Harper (AAH) model and from power-law systems with uncorrelated disorder. Whereas in the AAH model all single-particle states undergo a transition from ergodic to localized at a critical quasi-disorder strength, short-range power-law hops with $a>1$ can result in mobility edges. Interestingly, there is no localization for long-range hops with $a\leq 1$, in contrast to the case of uncorrelated disorder. Systems with long-range hops are rather characterized by ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but non ergodic) states. We show that both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.

- 1. TU/e - Eindhoven University of Technology [Eindhoven]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

### Maurizio Fagotti

^{1, 2}#### Maurizio Fagotti. On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system.

*SciPost Physics*, SciPost Foundation, 2019, 6 (5), ⟨10.21468/SciPostPhys.6.5.059⟩. ⟨hal-02292090⟩We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites $L^d$. We compute the distribution of the eigenvalues of the time averaged state over a time window $[t_0,t_0+t]$ in the limit of large $L$. This allows us to infer the size of a subspace that captures time evolution in $[t_0,t_0+t]$ with an accuracy $1-\epsilon$. We estimate the size to be $ \frac{\sqrt{2\mathfrak{e}_2}}{\pi}\mathrm{erf}^{-1}(1-\epsilon) L^{\frac{d}{2}}t$, where $\mathfrak{e}_2$ is the energy variance per site, and $\mathrm{erf}^{-1}$ is the inverse error function.

- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – On the number of limit cycles in asymmetric neural networks

### Sungmin Hwang

^{1}Viola Folli^{2}Enrico Lanza^{3}Giorgio Parisi^{3}Giancarlo Ruocco^{2, 3}Francesco Zamponi^{4}#### Sungmin Hwang, Viola Folli, Enrico Lanza, Giorgio Parisi, Giancarlo Ruocco, et al.. On the number of limit cycles in asymmetric neural networks.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (5), pp.053402. ⟨10.1088/1742-5468/ab11e3⟩. ⟨hal-02147155⟩The comprehension of the mechanisms at the basis of the functioning of complexly interconnected networks represents one of the main goals of neuroscience. In this work, we investigate how the structure of recurrent connectivity influences the ability of a network to have storable patterns and in particular limit cycles, by modeling a recurrent neural network with McCulloch-Pitts neurons as a content-addressable memory system. A key role in such models is played by the connectivity matrix, which, for neural networks, corresponds to a schematic representation of the "connectome": the set of chemical synapses and electrical junctions among neurons. The shape of the recurrent connectivity matrix plays a crucial role in the process of storing memories. This relation has already been exposed by the work of Tanaka and Edwards, which presents a theoretical approach to evaluate the mean number of fixed points in a fully connected model at thermodynamic limit. Interestingly, further studies on the same kind of model but with a finite number of nodes have shown how the symmetry parameter influences the types of attractors featured in the system. Our study extends the work of Tanaka and Edwards by providing a theoretical evaluation of the mean number of attractors of any given length L for different degrees of symmetry in the connectivity matrices.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Sapienza@IIT Laboratory - Center for Life Nano Science [Genova]
- 3. Università degli Studi di Roma "La Sapienza" [Rome]
- 4. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – On four-point connectivities in the critical 2d Potts model

### Marco Picco

^{1}Sylvain Ribault^{2}Raoul Santachiara^{3}#### Marco Picco, Sylvain Ribault, Raoul Santachiara. On four-point connectivities in the critical 2d Potts model.

*SciPost Phys.*, 2019, 7, pp.044. ⟨10.21468/SciPostPhys.7.4.044⟩. ⟨hal-02166498⟩We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the $2$ to $4$ significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane $\{\Re c <13\}$, where $c$ is the central charge of the Virasoro symmetry algebra.

- 1. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Noninteracting fermions in a trap and random matrix theory

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Gregory Schehr^{3, *}#### David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr. Noninteracting fermions in a trap and random matrix theory.

*Journal of Physics A: Mathematical and General*, IOP Publishing, 2019, 52 (14), pp.144006 (1-32). ⟨10.1088/1751-8121/ab098d⟩. ⟨hal-02102848⟩We review recent advances in the theory of trapped fermions using techniques borrowed from random matrix theory (RMT) and, more generally, from the theory of determinantal point processes. In the presence of a trap, and in the limit of a large number of fermions $N \gg 1$, the spatial density exhibits an edge, beyond which it vanishes. While the spatial correlations far from the edge, i.e. close to the center of the trap, are well described by standard many-body techniques, such as the local density approximation (LDA), these methods fail to describe the fluctuations close to the edge of the Fermi gas, where the density is very small and the fluctuations are thus enhanced. It turns out that RMT and determinantal point processes offer a powerful toolbox to study these edge properties in great detail. Here we discuss the principal edge universality classes, that have been recently identified using these modern tools. In dimension $d=1$ and at zero temperature $T=0$, these universality classes are in one-to-one correspondence with the standard universality classes found in the classical unitary random matrix ensembles: soft edge (described by the "Airy kernel") and hard edge (described by the "Bessel kernel") universality classes. We further discuss extensions of these results to higher dimensions $d\geq 2$ and to finite temperature. Finally, we discuss correlations in the phase space, i.e., in the space of positions and momenta, characterized by the so called Wigner function.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Nonequilibrium dynamics of noninteracting fermions in a trap

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Grégory Schehr^{3}#### David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr. Nonequilibrium dynamics of noninteracting fermions in a trap.

*EPL*, 2019, 126 (2), pp.20006. ⟨10.1209/0295-5075/126/20006⟩. ⟨hal-02165626⟩We consider the real-time dynamics of N noninteracting fermions in d = 1. They evolve in a trapping potential V(x), starting from the equilibrium state in a potential V 0(x). We study the time evolution of the Wigner function W(x, p, t) in the phase space (x, p), and the associated kernel which encodes all correlation functions. At t = 0 the Wigner function for large N is uniform in phase space inside the Fermi volume, and vanishes at the Fermi surf over a scale e N being described by a universal scaling function related to the Airy function. We obtain exact solutions for the Wigner function, the density, and the correlations in the case of harmonic and inverse square potentials, for several V 0(x). In the large-N limit, near the edges where the density vanishes, we obtain limiting kernels (of the Airy or Bessel types) that retain the form found in equilibrium, up to a time-dependent rescaling. For nonharmonic traps the evolution of the Fermi volume is more complex. Nevertheless we show that, for intermediate times, the Fermi surf is still described by the same equilibrium scaling function, with a nontrivial time- and space-dependent width which we compute analytically. We discuss the multi-time correlations and obtain their explicit scaling forms valid near the edge for the harmonic oscillator. Finally, we address the large-time limit where relaxation to the Generalized Gibbs Ensemble (GGE) was found to occur in the “classical” regime . Using the diagonal ensemble we compute the Wigner function in the quantum case (large N, fixed ℏ ) and show that it agrees with the GGE. We also obtain the higher order (nonlocal) correlations in the diagonal ensemble.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPENS - UMR 8023 - Laboratoire de physique de l'ENS - ENS Paris
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Noncrossing run-and-tumble particles on a line

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Pierre Le Doussal^{1}Satya Majumdar^{2}Gregory Schehr^{2}#### Pierre Le Doussal, Satya N. Majumdar, Pierre Le Doussal, Satya Majumdar, Gregory Schehr. Noncrossing run-and-tumble particles on a line.

*Physical Review E*, American Physical Society (APS), 2019, 100 (1), ⟨10.1103/PhysRevE.100.012113⟩. ⟨hal-02291902⟩We study active particles performing independent run and tumble motion on an infinite line with velocities $v_0 \sigma(t)$, where $\sigma(t) = \pm 1$ is a dichotomous telegraphic noise with constant flipping rate $\gamma$. We first consider one particle in the presence of an absorbing wall at $x=0$ and calculate the probability that it has survived up to time $t$ and is at position $x$ at time $t$. We then consider two particles with independent telegraphic noises and compute exactly the probability that they do not cross up to time $t$. Contrarily to the case of passive (Brownian) particles this two-RTP problem can not be reduced to a single RTP with an absorbing wall. Nevertheless, we are able to compute exactly the probability of no-crossing of two independent RTP's up to time $t$ and find that it decays at large time as $t^{-1/2}$ with an amplitude that depends on the initial condition. The latter allows to define an effective length scale, analogous to the so called `` Milne extrapolation length'' in neutron scattering, which we demonstrate to be a fingerprint of the active dynamics.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – New analysis of the free energy cost of interfaces in spin glasses

### Valerio Astuti

^{1}Silvio Franz^{2}Giorgio Parisi^{3}#### Valerio Astuti, Silvio Franz, Giorgio Parisi. New analysis of the free energy cost of interfaces in spin glasses.

*Journal of Physics A: Mathematical and General*, IOP Publishing, 2019, ⟨10.13013⟩. ⟨hal-02291847⟩In this work we want to enhance the calculation performed by Franz, Parisi and Virasoro (FPV) to estimate the free energy cost of interfaces in spin glasses and evaluate the lower critical dimension at which replica symmetry is restored. In particular we evaluate the free energy cost for a general class of effective Hamiltonians showing full replica symmetry breaking, and study the dependence of this cost on the order parameter and on the temperature. We confirm the findings of the FPV papers for the scaling of the free energy, recovering a value for the lower critical dimension of $D_{lc} = 2.5$. In addition to their results we find a non-trivial dependence of the free energy density cost on the order parameter and the temperature. Apart from the case of a restricted class of effective Hamiltonians this dependence cannot be expressed in terms of functions with a clear physical interpretation, as is the case in hierarchical models. In addition we connect the results on the lower critical dimension with recent simulations.

- 1. Dipartimento di Fisica, Università “La Sapienza"
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica

## Archive ouverte HAL – Multifractality of open quantum systems

### Agustín M. Bilen

^{1}Ignacio García-Mata^{1}Bertrand Georgeot^{2}Olivier Giraud^{3}#### Agustín M. Bilen, Ignacio García-Mata, Bertrand Georgeot, Olivier Giraud. Multifractality of open quantum systems.

*Physical Review E*, American Physical Society (APS), 2019, 100, pp.032223. ⟨10.1103/PhysRevE.100.032223⟩. ⟨hal-02156304⟩We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and we quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but these states are multifractal instead of ergodic at each level of the hierarchy. This is visible for sufficiently long-lived resonance states at scales smaller than the classical structures. Our results can guide experimentalists in order to observe multifractal behavior in open systems.

- 1. IFIMAR - Instituto de Investigaciones Físicas de Mar del Plata
- 2. Information et Chaos Quantiques (LPT)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Multi-Fluid Hydrodynamics in Charge Density Waves with Collective, Electronic, and Solitonic Densities and Currents

### S. Brazovskii

^{1}N. Kirova^{2}#### S. Brazovskii, N. Kirova. Multi-Fluid Hydrodynamics in Charge Density Waves with Collective, Electronic, and Solitonic Densities and Currents.

*Journal of Experimental and Theoretical Physics (JETP) / Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki*, MAIK Nauka/Interperiodica, 2019, 129 (4), pp.659-668. ⟨10.1134/S1063776119100017⟩. ⟨hal-02512280⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Archive ouverte HAL – Modeling the Correlated Activity of Neural Populations: A Review

### Christophe Gardella

^{1}Olivier Marre^{1}Thierry Mora^{2, 3}#### Christophe Gardella, Olivier Marre, Thierry Mora. Modeling the Correlated Activity of Neural Populations: A Review.

*Neural Computation*, Massachusetts Institute of Technology Press (MIT Press), 2019, 31 (2), pp.233-269. ⟨10.1162/neco_a_01154⟩. ⟨hal-02569955⟩- 1. Institut de la Vision
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Physique Statistique et Inférence pour la Biologie

## Archive ouverte HAL – Mechanical properties of lipid bilayers: a note on the Poisson ratio

### M. Mert Terzi

^{1}Markus Deserno^{2}John Nagle^{3}#### M. Mert Terzi, Markus Deserno, John Nagle. Mechanical properties of lipid bilayers: a note on the Poisson ratio.

*Soft Matter*, Royal Society of Chemistry, 2019, 15 (44), pp.9085-9092. ⟨10.1039/c9sm01290g⟩. ⟨hal-02512307⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CMU - Carnegie Mellon University [Pittsburgh]
- 3. University of Ulster

## Archive ouverte HAL – Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation

### Thibault Bonnemain

^{1, 2}Denis Ullmo^{1}#### Thibault Bonnemain, Denis Ullmo. Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation.

*Physica A: Statistical Mechanics and its Applications*, Elsevier, 2019, 523, pp.310-325. ⟨10.1016/j.physa.2019.01.143⟩. ⟨hal-02102129⟩Motivated by the study of a Mean Field Game toy model called the "seminar problem", we consider the Fokker-Planck equation in the small noise regime for a specific drift field. This gives us the opportunity to discuss the application to diffusion problem of the WKB approach "a la Maslov", making it possible to solve directly the time dependant problem in an especially transparent way.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTM - Laboratoire de Physique Théorique et Modélisation

## Archive ouverte HAL – Many-body localization in continuum systems: Two-dimensional bosons

### G. Bertoli

^{1}B. L. Altshuler^{2}G. V. Shlyapnikov^{1}#### G. Bertoli, B. L. Altshuler, G. V. Shlyapnikov. Many-body localization in continuum systems: Two-dimensional bosons.

*Physical Review A*, American Physical Society 2019, 100 (1), ⟨10.1103/PhysRevA.100.013628⟩. ⟨hal-02291788⟩We demonstrate that many-body localization of two-dimensional weakly interacting bosons in disorder remains stable in the thermodynamic limit at sufficiently low temperatures. Highly energetic particles destroy the localized state only above a critical temperature, which increases with the strength of the disorder. If the particle distribution is truncated at high energies, as it does for cold atom systems, the localization can be stable at any temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Physics Dept.

## Archive ouverte HAL – Long-time position distribution of an active Brownian particle in two dimensions

### Urna Basu

^{1}Satya N. Majumdar^{2}Alberto Rosso^{2}Satya Majumdar^{2}Gregory Schehr^{2}#### Urna Basu, Satya N. Majumdar, Alberto Rosso, Satya Majumdar, Gregory Schehr. Long-time position distribution of an active Brownian particle in two dimensions.

*Physical Review E*, American Physical Society (APS), 2019, 100 (6), ⟨10.1103/PhysRevE.100.062116⟩. ⟨hal-02512255⟩We study the late time dynamics of a single active Brownian particle in two dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that at late times $t\gg D_R^{-1}$, while the position probability distribution $P(x,y,t)$ in the $x$-$y$ plane approaches a Gaussian form near its peak describing the typical diffusive fluctuations, it has non-Gaussian tails describing atypical rare fluctuations when $\sqrt{x^2+y^2}\sim v_0 t$. In this regime, the distribution admits a large deviation form, $P(x,y,t) \sim \exp\left[-t\, D_R\, \Phi\left(\sqrt{x^2+y^2}/(v_0 t)\right)\right]$, where we compute the rate function $\Phi(z)$ analytically and also numerically using an importance sampling method. We show that the rate function $\Phi(z)$, encoding the rare fluctuations, still carries the trace of activity even at late times. Another way of detecting activity at late times is to subject the active particle to an external harmonic potential. In this case we show that the stationary distribution $P_\text{stat}(x,y)$ depends explicitly on the activity parameter $D_R^{-1}$ and undergoes a crossover, as $D_R$ increases, from a ring shape in the strongly active limit ($D_R\to 0$) to a Gaussian shape in the strongly passive limit $(D_R\to \infty)$.

- 1. Theoretical Condensed Matter Physics Division
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method

### M. Isoard

^{1}A. M. Kamchatnov^{2}N. Pavloff^{1}*Physical Review E*, American Physical Society (APS), 2019, 〈10.07952〉We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton, but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute of Spectroscopy

## Archive ouverte HAL – Lattice Boltzmann Electrokinetics simulation of nanocapacitors

### Adelchi J. Asta

^{1}Ivan Palaia^{2}Emmanuel Trizac^{2}Maximilien Levesque^{3}Benjamin Rotenberg^{4}#### Adelchi J. Asta, Ivan Palaia, Emmanuel Trizac, Maximilien Levesque, Benjamin Rotenberg. Lattice Boltzmann Electrokinetics simulation of nanocapacitors.

*Journal of Chemical Physics*, American Institute of Physics, 2019. ⟨hal-02295839⟩We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics simulations (LBE), a lattice-based algorithm rooted in kinetic theory which captures the coupled solvent and ion dynamics in electrolyte solutions. This is achieved by a simple rule to impose electrostatic boundary conditions, in a consistent way with the location of the hydrodynamic interface for stick boundary conditions. The proposed method also provides the local charge induced on the electrode by the instantaneous distribution of ions under voltage. We validate it in the low voltage regime by comparison with analytical results in two model nanocapacitors: parallel plate and coaxial electrodes. We examine the steady-state ionic concentrations and electric potential profiles (and corresponding capacitance), the time-dependent response of the charge on the electrodes, as well as the steady-state electro-osmotic profiles in the presence of an additional, tangential electric field. The LBE method further provides the time-dependence of these quantities, as illustrated on the electro-osmotic response. While we do not consider this case in the present work, which focuses on the validation of the method, the latter readily applies to large voltages between the electrodes, as well as to time-dependent voltages. This work opens the way to the LBE simulation of more complex systems involving electrodes and metallic surfaces, such as sensing devices based on nanofluidic channels and nanotubes, or porous electrodes.

- 1. PHENIX - PHysicochimie des Electrolytes et Nanosystèmes InterfaciauX
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PASTEUR - Processus d'Activation Sélective par Transfert d'Energie Uni-électronique ou Radiatif (UMR 8640)
- 4. PECSA - Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques

## Archive ouverte HAL – Jamming in Multilayer Supervised Learning Models

### Silvio Franz

^{1}Sungmin Hwang^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Sungmin Hwang, Pierfrancesco Urbani. Jamming in Multilayer Supervised Learning Models.

*Physical Review Letters*, American Physical Society, 2019, 123 (16), ⟨10.1103/PhysRevLett.123.160602⟩. ⟨hal-02395521⟩Critical jamming transitions are characterized by an astonishing degree of universality. Analytic and numerical evidence points to the existence of a large universality class that encompasses finite and infinite dimensional spheres and continuous constraint satisfaction problems (CCSP) such as the non-convex perceptron and related models. In this paper we investigate multilayer neural networks (MLNN) learning random associations as models for CCSP which could potentially define different jamming universality classes. As opposed to simple perceptrons and infinite dimensional spheres, which are described by a single effective field in terms of which the constraints appear to be one-dimensional, the description of MLNN, involves multiple fields, and the constraints acquire a multidimensional character. We first study the models numerically and show that similarly to the perceptron, whenever jamming is isostatic, the sphere universality class is recovered, we then write the exact mean-field equations for the models and identify a dimensional reduction mechanism that leads to a scaling regime identical to one of the infinite dimensional spheres. We suggest that this mechanism could be general enough to explain finite dimensional universality.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Archive ouverte HAL – Intertwined chiral charge orders and topological stabilization of the light-induced state of a prototypical transition metal dichalcogenide

### Yaroslav A. GerasimenkoPeter KarpovIgor Vaskivskyi

^{1}Serguei Brazovskii^{2}Dragan Mihailovic^{3}Yaroslav GerasimenkoPetr Karpov^{4}#### Yaroslav A. Gerasimenko, Peter Karpov, Igor Vaskivskyi, Serguei Brazovskii, Dragan Mihailovic, et al.. Intertwined chiral charge orders and topological stabilization of the light-induced state of a prototypical transition metal dichalcogenide.

*NPJ QUANTUM MATERIALS*, 2019, 4 (1), ⟨10.1038/s41535-019-0172-1⟩. ⟨hal-02421684⟩The fundamental idea that the constituents of interacting many body systems in complex quantum materials may self-organise into long range order under highly non-equilibrium conditions leads to the notion that entirely new and unexpected functionalities might be artificially created. However, demonstrating new emergent order in highly non-equilibrium transitions has proven surprisingly difficult. In spite of huge recent advances in experimental ultrafast time-resolved techniques, methods that average over successive transition outcomes have so far proved incapable of elucidating the emerging spatial structure. Here, using scanning tunneling microscopy, we report for the first time the charge order emerging after a single transition outcome in a prototypical two-dimensional dichalcogenide 1T-TaS$_2$ initiated by a single optical pulse. By mapping the vector field of charge displacements of the emergent state, we find surprisingly intricate, long-range, topologically non-trivial charge order in which chiral domain tiling is intertwined with unique unpaired dislocations which play a crucial role in enhancing the emergent states remarkable stability. The discovery of the principles that lead to metastability in charge-ordered systems open the way to designing novel emergent functionalities, particularly ultrafast all-electronic non-volatile cryo-memories.

- 1. University of Ljubljana
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. CENN Nanocenter
- 4. MISIS - National University of Science and Technology

## Archive ouverte HAL – Intermediate deviation regime for the full eigenvalue statistics in the complex Ginibre ensemble

### Bertrand Lacroix-A-Chez-Toine

^{1}Jeyson Andres Monroy GarzonChristopher Sebastian Hidalgo CalvaAnupam Kundu^{2}Satya N. Majumdar^{1}Jeyson Andrés Monroy GarzónIsaac Pérez Castillo^{3}Satya Majumdar^{1}Gregory Schehr^{1}#### Bertrand Lacroix-A-Chez-Toine, Jeyson Andres Monroy Garzon, Christopher Sebastian Hidalgo Calva, Anupam Kundu, Satya N. Majumdar, et al.. Intermediate deviation regime for the full eigenvalue statistics in the complex Ginibre ensemble.

*Physical Review E*, American Physical Society (APS), 2019, 100 (1), ⟨10.1103/PhysRevE.100.012137⟩. ⟨hal-02291786⟩We study the Ginibre ensemble of $N \times N$ complex random matrices and compute exactly, for any finite $N$, the full distribution as well as all the cumulants of the number $N_r$ of eigenvalues within a disk of radius $r$ centered at the origin. In the limit of large $N$, when the average density of eigenvalues becomes uniform over the unit disk, we show that for $0

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 3. Departamento de Sistemas Complejos, Instituto de Física, UNAM

## Archive ouverte HAL – Impact of jamming criticality on low-temperature anomalies in structural glasses

### Silvio Franz

^{1}Thibaud Maimbourg^{2, 1}Giorgio Parisi^{3}Antonello Scardicchio^{4}#### Silvio Franz, Thibaud Maimbourg, Giorgio Parisi, Antonello Scardicchio. Impact of jamming criticality on low-temperature anomalies in structural glasses.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2019, 116 (28), pp.13768-13773. ⟨10.1073/pnas.1820360116⟩. ⟨hal-02292219⟩We present a novel mechanism for the anomalous behaviour of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a crossover temperature above which the specific heat scales linearly with temperature while below it a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) The marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling (ii) The vicinity of the classical jamming critical point, as the crossover temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals, the Debye approximation does not hold.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica
- 4. ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]

## Archive ouverte HAL – How many different clonotypes do immune repertoires contain?

### Thierry Mora

^{1, 2}Aleksandra Walczak^{2}#### Thierry Mora, Aleksandra Walczak. How many different clonotypes do immune repertoires contain?.

*Current Opinion in Systems Biology*, Elsevier, 2019, 18, pp.104-110. ⟨10.1016/j.coisb.2019.10.001⟩. ⟨hal-02569976⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Physique Statistique et Inférence pour la Biologie

## Archive ouverte HAL – How collective asperity detachments nucleate slip at frictional interfaces

### Tom W. J. de GeusMarko Popović

^{1}Wencheng JiAlberto Rosso^{2}Matthieu Wyart^{3}#### Tom W. J. de Geus, Marko Popović, Wencheng Ji, Alberto Rosso, Matthieu Wyart. How collective asperity detachments nucleate slip at frictional interfaces.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2019. ⟨hal-02395574⟩Sliding at a quasi-statically loaded frictional interface occurs via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_\sigma$ presents a pseudo-gap $P(x_\sigma) \sim (x_\sigma)^\theta$, where $\theta$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $\theta$-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

- 1. MPI-PKS - Max Planck Institute for the Physics of Complex Systems
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. EPFL - Ecole Polytechnique Fédérale de Lausanne

## Archive ouverte HAL – High-temperature expansions and message passing algorithms

### Antoine Maillard

^{1, *}Laura Foini^{2}Alejandro Lage Castellanos^{3}Florent Krzakala^{1}Marc Mezard^{4}Lenka Zdeborová^{2}#### Antoine Maillard, Laura Foini, Alejandro Lage Castellanos, Florent Krzakala, Marc Mezard, et al.. High-temperature expansions and message passing algorithms.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (11), pp.113301. ⟨10.1088/1742-5468/ab4bbb⟩. ⟨cea-02524865⟩Improved mean-eld technics are a central theme of statistical physics methods applied to inference and learning. We revisit here some of these methods using high-temperature expansions for disordered systems initiated by Plefka, Georges and Yedidia. We derive the Gibbs free entropy and the subsequent self-consistent equations for a generic class of statistical models with correlated matrices and show in particular that many classical approximation schemes, such as adaptive TAP, Expectation-Consistency, or the approximations behind the Vector Approximate Message Passing algorithm all rely on the same assumptions, that are also at the heart of high-temperature expansions. We focus on the case of rotationally invariant random coupling matrices in the 'high-dimensional' limit in which the number of samples and the dimension are both large, but with a xed ratio. This encapsulates many widely studied models, such as Restricted Boltzmann Machines or Generalized Linear Models with correlated data matrices. In this general setting, we show that all the approximation schemes described before are equivalent, and we conjecture that they are exact in the thermodynamic limit in the replica symmetric phases. We achieve this conclusion by resummation of the in nite perturbation series, which generalises a seminal result of Parisi and Potters. A rigorous derivation of this conjecture is an interesting mathematical challenge. On the way to these conclusions, we uncover several diagrammatical results in connection with free probability and random matrix theory, that are interesting independently of the rest of our work.

- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 3. University of Havana - Departamento de Física Teórica
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Harmonically Confined Particles with Long-Range Repulsive Interactions

### Sanaa AgarwalAbhishek Dhar

^{1}Manas KulkarniAnupam Kundu^{1}Satya N. Majumdar^{2}David Mukamel^{3}Gregory Schehr^{2}S. n. Majumdar#### Sanaa Agarwal, Abhishek Dhar, Manas Kulkarni, Anupam Kundu, Satya N. Majumdar, et al.. Harmonically Confined Particles with Long-Range Repulsive Interactions.

*Physical Review Letters*, American Physical Society, 2019, 123 (10), ⟨10.1103/PhysRevLett.123.100603⟩. ⟨hal-02295905⟩We study an interacting system of $N$ classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law $\propto \sum_{\substack{i\neq j}}^N|x_i-x_j|^{-k}$ (with $k>-2$) of their mutual distance. This is a generalization of the well known cases of the one component plasma ($k=-1$), Dyson's log-gas ($k\to 0^+$), and the Calogero-Moser model ($k=2$). Due to the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all $k>-2$. We compute exactly the average density profile for large $N$ for all $k>-2$ and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on $k$ with distinct behavior for $-2

- 1. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Weizmann Institute

## Archive ouverte HAL – Gap statistics close to the quantile of a random walk

### Bertrand Lacroix-A-Chez-Toine

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}Satya Majumdar^{1}#### Bertrand Lacroix-A-Chez-Toine, Satya N. Majumdar, Gregory Schehr, Satya Majumdar. Gap statistics close to the quantile of a random walk.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (31), pp.315003. ⟨10.1088/1751-8121/ab2cf9⟩. ⟨hal-02291855⟩We consider a random walk of $n$ steps starting at $x_0=0$ with a double exponential (Laplace) jump distribution. We compute exactly the distribution $p_{k,n}(\Delta)$ of the gap $d_{k,n}$ between the $k^{\rm th}$ and $(k+1)^{\rm th}$ maxima in the limit of large $n$ and large $k$, with $\alpha=k/n$ fixed. We show that the typical fluctuations of the gaps, which are of order $O( n^{-1/2})$, are described by a universal $\alpha$-dependent distribution, which we compute explicitly. Interestingly, this distribution has an inverse cubic tail, which implies a non-trivial $n$-dependence of the moments of the gaps. We also argue, based on numerical simulations, that this distribution is universal, i.e. it holds for more general jump distributions (not only the Laplace distribution), which are continuous, symmetric with a well defined second moment. Finally, we also compute the large deviation form of the gap distribution $p_{\alpha n,n}(\Delta)$ for $\Delta=O(1)$, which turns out to be non-universal.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – From chiral anomaly to two-fluid hydrodynamics for electronic vortices

### S. Brazovskii

^{1}N. Kirova^{2}*Annals Phys.*, 2019, 403, pp.184-197. 〈10.1016/j.aop.2018.07.004〉Many recent experiments addressed manifestations of electronic crystals, particularly the charge density waves, in nano-junctions, under electric field effect, at high magnetic fields, together with real space visualizations by STM and micro X-ray diffraction. This activity returns the interest to stationary or transient states with static and dynamic topologically nontrivial configurations: electronic vortices as dislocations, instantons as phase slip centers, and ensembles of microscopic solitons. Describing and modeling these states and processes calls for an efficient phenomenological theory which should take into account the degenerate order parameter, various kinds of normal carriers and the electric field. Here we notice that the commonly employed time-depend Ginzburg–Landau approach suffers with violation of the charge conservation law resulting in unphysical generation of particles which is particularly strong for nucleating or moving electronic vortices. We present a consistent theory which exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The resulting equations clarify partitions of charges, currents and rigidity among subsystems of the condensate and normal carriers. On this basis we perform the numerical modeling of a spontaneously generated coherent sequence of phase slips – the spacetime vortices – serving for the conversion among the injected normal current and the collective one.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Archive ouverte HAL – Free fermions and α -determinantal processes

### Fabio Deelan Cunden

^{1}Satya N. Majumdar^{2}Neil O'Connell^{1}#### Fabio Deelan Cunden, Satya N. Majumdar, Neil O'Connell. Free fermions and α -determinantal processes.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (16), pp.165202. ⟨10.1088/1751-8121/ab0ebd⟩. ⟨hal-02102134⟩The $\alpha$-determinant is a one-parameter generalisation of the standard determinant, with $\alpha=-1$ corresponding to the determinant, and $\alpha=1$ corresponding to the permanent. In this paper a simple limit procedure to construct $\alpha$-determinantal point processes out of fermionic processes is examined. The procedure is illustrated for a model of $N$ free fermions in a harmonic potential. When the system is in the ground state, the rescaled correlation functions converge for large $N$ to determinants (of the sine kernel in the bulk and the Airy kernel at the edges). We analyse the point processes associated to a special family of excited states of fermions and show that appropriate scaling limits generate $\alpha$-determinantal processes. Links with wave optics and other random matrix models are suggested.

- 1. UCD - University College Dublin [Dublin]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Free energy of cylindrical polyions: Analytical results

### Emmanuel Trizac

^{1}Gabriel Tellez^{2}#### Emmanuel Trizac, Gabriel Tellez. Free energy of cylindrical polyions: Analytical results.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 151 (12), pp.124904. ⟨10.1063/1.5121724⟩. ⟨hal-02395512⟩Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged soft matter problems, we work out the Coulombic grand potential of a long cylindrical charged polyion in a binary electrolyte solution of arbitrary valency and for low salt concentration. We obtain the exact analytical low-salt asymptotic expression for the grand potential, derived from known properties of the exact solutions to the cylindrical PB equation. These results are relevant for understanding nucleic acid processes. In practice, our expressions are accurate for arbitrary polyion charges, provided their radius is smaller than the Debye length defined by the electrolyte.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departamento de Fisica

## Archive ouverte HAL – Fluctuation-dominated phase ordering at a mixed order transition

### Mustansir Barma

^{1}Satya N. Majumdar^{2}David Mukamel^{3}Satya Majumdar^{2}#### Mustansir Barma, Satya N. Majumdar, David Mukamel, Satya Majumdar. Fluctuation-dominated phase ordering at a mixed order transition.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (25), pp.254001. ⟨10.1088/1751-8121/ab2064⟩. ⟨hal-02291900⟩Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.

- 1. Department of Theoretical Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Weizmann Institute

## Archive ouverte HAL – Fiber plucking by molecular motors yields large emergent contractility in stiff biopolymer networks

### Pierre Ronceray

^{1}Chase P. Broedersz^{2}Martin Lenz^{3, 4}*Soft Matter*, Royal Society of Chemistry, 2019The mechanical properties of the cell depend crucially on the tension of its cytoskeleton, a biopolymer network that is put under stress by active motor proteins. While the fibrous nature of the network is known to strongly affect the transmission of these forces to the cellular scale, our understanding of this process remains incomplete. Here we investigate the transmission of forces through the network at the individual filament level, and show that active forces can be geometrically amplified as a transverse motor-generated force force "plucks" the fiber and induces a nonlinear tension. In stiff and densely connnected networks, this tension results in large network-wide tensile stresses that far exceed the expectation drawn from a linear elastic theory. This amplification mechanism competes with a recently characterized network-level amplification due to fiber buckling, suggesting that that fiber networks provide several distinct pathways for living systems to amplify their molecular forces.

- 1. Princeton Center for Theoretical Science
- 2. LMU - Ludwig-Maximilians-Universität München
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment

## Archive ouverte HAL – Fermi surface enlargement on the Kondo lattice

### Eoin Quinn

^{1}Onur Erten#### Eoin Quinn, Onur Erten. Fermi surface enlargement on the Kondo lattice.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 99 (24), ⟨10.1103/PhysRevB.99.245123⟩. ⟨hal-02291818⟩The Kondo lattice model is a paradigmatic model for the description of local moment systems, a class of materials exhibiting a range of strongly correlated phenomena including heavy fermion formation, magnetism, quantum criticality and unconventional superconductivity. Conventional theoretical approaches invoke fractionalization of the local moment spin through large-N and slave particle methods. In this work we develop a new formalism, based instead on non-canonical degrees of freedom. We demonstrate that the graded Lie algebra su(2|2) provides a powerful means of organizing correlations on the Kondo lattice through a splitting of the electronic degree of freedom, in a manner which entwines the conduction electrons with the local moment spins. This offers a novel perspective on heavy fermion formation. Unlike slave-particle methods, non-canonical degrees of freedom generically allow for a violation of the Luttinger sum rule, and we interpret recent angle resolved photoemission experiments on Ce-115 systems in view of this.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Fault Heterogeneity and the Connection between Aftershocks and Afterslip

### Eugenio LippielloGiuseppe PetrilloFrançois Landes

^{1, 2, 3}Alberto Rosso^{4}#### Eugenio Lippiello, Giuseppe Petrillo, François Landes, Alberto Rosso. Fault Heterogeneity and the Connection between Aftershocks and Afterslip.

*Bulletin of the Seismological Society of America*, Seismological Society of America, 2019, 109 (3), pp.1156-1163. ⟨10.1785/0120180244⟩. ⟨hal-02156407⟩- 1. LRI - Laboratoire de Recherche en Informatique
- 2. TAU - TAckling the Underspecified
- 3. UP11 UFR Sciences - Université Paris-Sud 11 - Faculté des Sciences
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

### A. Maitra

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1}#### A. Maitra, D. Leibfried, D. Ullmo, H. Landa. Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps.

*Physical Review A*, American Physical Society 2019, 99 (4), ⟨10.1103/PhysRevA.99.043421⟩. ⟨hal-02291892⟩We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technology [Gaithersburg]

## Archive ouverte HAL – Exclusion Statistics and lattice random walks

### Stéphane Ouvry

^{1}Alexios Polychronakos^{2}#### Stéphane Ouvry, Alexios Polychronakos. Exclusion Statistics and lattice random walks.

*Nuclear Physics B*, Elsevier, 2019, 949, pp.114797. ⟨10.1016/j.nuclphysb.2019.114731⟩. ⟨hal-02409911⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Physics Department

## Archive ouverte HAL – Exactly Solvable Record Model for Rainfall

### Satya N. Majumdar

^{1}Philipp von BomhardJoachim Krug^{2}Satya Majumdar^{1}#### Satya N. Majumdar, Philipp von Bomhard, Joachim Krug, Satya Majumdar. Exactly Solvable Record Model for Rainfall.

*Physical Review Letters*, American Physical Society, 2019, 122 (15), ⟨10.1103/PhysRevLett.122.158702⟩. ⟨hal-02291862⟩Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability $p$, we show that the presence of dry days induces negative correlations between record-breaking precipitation events. The resulting non-monotonic behavior of the Fano factor of the record counting process is recovered in empirical data. We derive the full probability distribution $P(R,n)$ of the number of records $R_n$ up to time $n$, and show that for large $n$, its large deviation form coincides with that of a Poisson distribution with parameter $\ln(p\,n)$. We also study in detail the joint limit $p \to 0$, $n \to \infty$, which yields a random record model in continuous time $t = pn$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Cologne

## Archive ouverte HAL – Enhancement of many-body quantum interference in chaotic bosonic systems

### Peter Schlagheck

^{1}Denis Ullmo^{2}Juan Diego Urbina^{3}Klaus RichterSteven Tomsovic^{4}#### Peter Schlagheck, Denis Ullmo, Juan Diego Urbina, Klaus Richter, Steven Tomsovic. Enhancement of many-body quantum interference in chaotic bosonic systems.

*Physical Review Letters*, American Physical Society, 2019, 123, pp.215302. ⟨10.1103/PhysRevLett.123.215302⟩. ⟨hal-02361335⟩Although highly successful, the truncated Wigner approximation (TWA) leaves out many-body quantum interference between mean-field Gross-Pitaevskii solutions as well as other quantum effects, and is therefore essentially classical. Turned around, this implies that if a system's quantum properties deviate from TWA, they must be exhibiting some quantum phenomenon, such as localization, diffraction, or tunneling. Here, we consider in detail a particular interference effect arising from discrete symmetries, which can lead to a significant enhancement of quantum observables with respect to the TWA prediction, and derive an augmented version of the TWA in order to incorporate them. Using the Bose-Hubbard model for illustration, we further show strong evidence for the presence of dynamical localization due to remaining differences between the TWA predictions and quantum results.

- 1. Institut für Theoretische Physik
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. UR - Universität Regensburg
- 4. Department of Physics

## Archive ouverte HAL – Electrophoresis of active Janus particles

### Parvin Bayati

^{1}Ali Najafi#### Parvin Bayati, Ali Najafi. Electrophoresis of active Janus particles.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 150 (23), pp.234902. ⟨10.1063/1.5101023⟩. ⟨hal-02291804⟩We theoretically consider the dynamics of a self-propelled active Janus motor moving in an external electric field. The external field can manipulate the route of a Janus particle and enforce it to move towards the desired targets. To investigate the trajectory of this active motor, we use a perturbative scheme. At the leading orders of surface activity of the Janus particle and also the external field, the orientational dynamics of the Janus particles behave like a mathematical pendulum with an angular the velocity that is sensitive to both the electric field and surface activity of the motor.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Electromagnetic surface wave propagation in a metallic wire and the Lambert W function

### J. Ricardo G. Mendonça

^{1}#### J. Ricardo G. Mendonça. Electromagnetic surface wave propagation in a metallic wire and the Lambert W function.

*American Journal of Physics*, American Association of Physics Teachers, 2019, 87 (6), pp.476-484. ⟨10.1119/1.5100943⟩. ⟨hal-02291821⟩We revisit the solution due to Sommerfeld of a problem in classical electrodynamics, namely, that of the propagation of an electromagnetic axially symmetric surface wave (a low-attenuation single TM$_{01}$ mode) in a cylindrical metallic wire, and his iterative method to solve the transcendental equation that appears in the determination of the propagation wave number from the boundary conditions. We present an elementary analysis of the convergence of Sommerfeld's iterative solution of the approximate problem and compare it with both the numerical solution of the exact transcendental equation and the solution of the approximate problem by means of the Lambert $W$ function.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Electric double layers with surface charge modulations: Novel exact Poisson-Boltzmann solutions

### L. Samaj

^{1}E. Trizac^{2}#### L. Samaj, E. Trizac. Electric double layers with surface charge modulations: Novel exact Poisson-Boltzmann solutions.

*Physical Review E*, American Physical Society (APS), 2019, ⟨10.02870⟩. ⟨hal-02421677⟩Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide novel exact analytical solutions to this non-linear mean-field approach, for the diffuse layer of ions in the vicinity of a planar or a cylindrical macroion. While previously known solution are for homogeneously charged objects, the cases worked out exhibit a modulated surface charge --or equivalently surface potential-- on the macroion (wall) surface. In addition to asymptotic features at large distances from the wall, attention is paid to the fate of the contact theorem, relating the contact density of ions to the local wall charge density. For salt-free systems (counterions only), we make use of results pertaining to the two-dimensional Liouville equation, supplemented by an inverse approach. When salt is present, we invoke the exact two-soliton solution to the 2D sinh-Gordon equation. This leads to inhomogeneous charge patterns, that are either localized or periodic in space. Without salt, the electrostatic signature of a charge pattern on the macroion fades exponentially with distance for a planar macroion, while it decays as an inverse power-law for a cylindrical macroion. With salt, our study is limited to the planar geometry, and reveals that pattern screening is exponential.

- 1. INSTITUTE OF PHYSICS - SLOVAK ACADEMY OF SCIENCES Institute of Physics Dubraska cesta 9, 84228 Bratislava, Slovaquie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

### Grégoire Misguich

^{1}Nicolas Pavloff^{2}Vincent Pasquier^{1}#### Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier. Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point.

*SciPost Physics*, SciPost Foundation, 2019, 7 (2), ⟨10.21468/SciPostPhys.7.2.025⟩. ⟨hal-02295825⟩We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.

- 1. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Distribution of Brownian coincidences

### Alexandre Krajenbrink

^{1}Bertrand Lacroix-A-Chez-Toine^{2}Pierre Le Doussal^{3}#### Alexandre Krajenbrink, Bertrand Lacroix-A-Chez-Toine, Pierre Le Doussal. Distribution of Brownian coincidences.

*Journal of Statistical Physics*, Springer Verlag, 2019. ⟨hal-02295902⟩We study the probability distribution, $P_N(T)$, of the coincidence time $T$, i.e. the total local time of all pairwise coincidences of $N$ independent Brownian walkers. We consider in details two geometries: Brownian motions all starting from $0$, and Brownian bridges. Using a Feynman-Kac representation for the moment generating function of this coincidence time, we map this problem onto some observables in three related models (i) the propagator of the Lieb Liniger model of quantum particles with pairwise delta function interactions (ii) the moments of the partition function of a directed polymer in a random medium (iii) the exponential moments of the solution of the Kardar-Parisi-Zhang equation. Using these mappings, we obtain closed formulae for the probability distribution of the coincidence time, its tails and some of its moments. Its asymptotics at large and small coincidence time are also obtained for arbitrary fixed endpoints. The universal large $T$ tail, $P_N(T) \sim \exp(- 3 T^2/(N^3-N))$ is obtained, and is independent of the geometry. We investigate the large deviations in the limit of a large number of walkers through a Coulomb gas approach. Some of our analytical results are compared with numerical simulations.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Darcy’s Law for Yield Stress Fluids

### Chen Liu

^{1}Andrea de Luca^{2}Alberto Rosso^{3}Laurent Talon^{1}#### Chen Liu, Andrea de Luca, Alberto Rosso, Laurent Talon. Darcy’s Law for Yield Stress Fluids.

*Physical Review Letters*, American Physical Society, 2019, 122 (24), ⟨10.1103/PhysRevLett.122.245502⟩. ⟨hal-02165315⟩- 1. FAST - Fluides, automatique, systèmes thermiques
- 2. Rudolf Peierls Center for Theoretical Physics
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Critical Jammed Phase of the Linear Perceptron

### Silvio Franz

^{1}Antonio Sclocchi^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Critical Jammed Phase of the Linear Perceptron.

*Physical Review Letters*, American Physical Society, 2019, 123 (11), ⟨10.1103/PhysRevLett.123.115702⟩. ⟨hal-02292061⟩Criticality in statistical physics naturally emerges at isolated points in the phase diagram. Jamming of spheres is not an exception: varying density, it is the critical point that separates the unjammed phase where spheres do not overlap and the jammed phase where they cannot be arranged without overlaps. The same remains true in more general constraint satisfaction problems with continuous variables (CCSP) where jamming coincides with the (protocol dependent) satisfiability transition point. In this work we show that by carefully choosing the cost function to be minimized, the region of criticality extends to occupy a whole region of the jammed phase. As a working example, we consider the spherical perceptron with a linear cost function in the unsatisfiable (UNSAT) jammed phase and we perform numerical simulations which show critical power laws emerging in the configurations obtained minimizing the linear cost function. We develop a scaling theory to compute the emerging critical exponents.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Archive ouverte HAL – Correlated Rigidity Percolation and Colloidal Gels

### Shang ZhangLeyou ZhangMehdi Bouzid

^{1, 2}D. Zeb RocklinEmanuela del Gado^{3}Xiaoming Mao^{4}#### Shang Zhang, Leyou Zhang, Mehdi Bouzid, D. Zeb Rocklin, Emanuela del Gado, et al.. Correlated Rigidity Percolation and Colloidal Gels.

*Physical Review Letters*, American Physical Society, 2019, 123 (5), ⟨10.1103/PhysRevLett.123.058001⟩. ⟨hal-02291872⟩Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.

- 1. PMMH - Physique et mécanique des milieux hétérogenes
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LCVN - Laboratoire des colloïdes, verres et nanomatériaux
- 4. UIUC - Physics Department

## Archive ouverte HAL – Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems

### Ada Altieri

^{1}Silvio Franz^{2}*Physical Review E*, American Physical Society (APS), 2019, 99 (1), 〈10.1103/PhysRevE.99.010401〉We discuss a resource-competition model, which takes the MacArthur's model as a platform, to unveil interesting connections with glassy features and jamming in high dimension. This model presents two qualitatively different phases: a "shielded" phase, where a collective and self-sustained behavior emerges, and a "vulnerable" phase, where a small perturbation can destabilize the system and contribute to population extinction. We first present our perspective based on a strong similarity with continuous constraint satisfaction problems in their convex regime. Then, we discuss the stability in terms of the computation of the leading eigenvalue of the Hessian matrix of the free energy in the replica space. This computation allows us to efficiently distinguish between the two aforementioned phases and to relate high-dimensional critical ecosystems to glassy phenomena in the low-temperature regime.

- 1. LPS - Laboratoire de Physique Statistique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Comparing dynamics: deep neural networks versus glassy systems

### Marco Baity-Jesi

^{1}Levent Sagun^{2}Mario Geiger^{3}Stefano Spigler^{4}Gérard Ben Arous^{5}Chiara Cammarota^{6}Yann Lecun^{7}Matthieu Wyart^{3}Giulio Biroli^{8, 9, 10}#### Marco Baity-Jesi, Levent Sagun, Mario Geiger, Stefano Spigler, Gérard Ben Arous, et al.. Comparing dynamics: deep neural networks versus glassy systems.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (12), pp.124013. ⟨10.1088/1742-5468/ab3281⟩. ⟨hal-02569114⟩- 1. Department of Physics and Astronomy [Philadelphia]
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 3. EPFL - Ecole Polytechnique Fédérale de Lausanne
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. IMA - Institut de Mathématiques
- 6. King‘s College London
- 7. FAIR - Facebook AI Research [Paris]
- 8. SPhT - Service de Physique Théorique
- 9. LPS - Laboratoire de Physique Statistique de l'ENS
- 10. Systèmes Désordonnés et Applications

## Archive ouverte HAL – Can a periodically driven particle resist laser cooling and noise?

### A. Maitra

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1}#### A. Maitra, D. Leibfried, D. Ullmo, H. Landa. Can a periodically driven particle resist laser cooling and noise?.

*Physical Review Research*, American Physical Society, 2019, ⟨10.01856⟩. ⟨hal-02395528⟩Studying a single atomic ion confined in a time-dependent periodic anharmonic potential, we find large amplitude trajectories stable for millions of oscillation periods in the presence of stochastic laser cooling. The competition between energy gain from the time-dependent drive and damping leads to the stabilization of such stochastic limit cycles. Instead of converging to the global minimum of the averaged potential, the steady-state phase-space distribution develops multiple peaks in the regions of phase space where the frequency of the motion is close to a multiple of the periodic drive. Such distinct nonequilibrium behaviour can be observed in realistic radio-frequency traps with laser-cooled ions, suggesting that Paul traps offer a well-controlled test-bed for studying transport and dynamics of microscopically driven systems.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technology [Gaithersburg]

## Archive ouverte HAL – Bulk organic aerosol analysis by PTR-MS: an improved methodology for the determination of total organic mass, O:C and H:C ele- mental ratios and the average molecular formula

### Joris Leglise

^{1}Markus Muller^{2}Felix Piel^{3}Tobias Otto^{4}Armin Wisthaler^{5, 6}#### Joris Leglise, Markus Muller, Felix Piel, Tobias Otto, Armin Wisthaler. Bulk organic aerosol analysis by PTR-MS: an improved methodology for the determination of total organic mass, O:C and H:C ele- mental ratios and the average molecular formula.

*Analytical Chemistry*, American Chemical Society, 2019, ⟨10.1021/acs.analchem.9b02949⟩. ⟨hal-02459530⟩We have recently shown in this journal (Müller et al., Anal. Chem. 2017, 89, 10889-10897) how a proton-transfer-reaction mass spectrometry (PTR-MS) analyzer measured particulate organic matter in urban atmospheres using the "Chemical Analysis of Aerosol Online" (CHARON) inlet. Our initial CHARON studies did not take into account fragmentation of protonated analyte molecules, which introduced a small but significant negative bias in the determination of bulk organic aerosol parameters. Herein, we studied the ionic fragmentation of 26 oxidized organic compounds typically found in atmospheric particles. This allowed us to derive a correction algorithm for the determination of the bulk organic mass concentration, m OA , the bulk-average hydrogen to carbon ratio, (H:C) bulk, the bulk-average oxygen-to-carbon, (O:C) bulk , and the bulk-average molecular formula, MF bulk. The correction algorithm was validated against AMS data using two sets of published data. Finally, we determined MF bulk of particles generated from the reaction of -pinene and ozone and compared and discussed the results in relation to the literature.

- 1. ICARE - Institut de Combustion, Aérothermique, Réactivité et Environnement
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IAU - Institute for Atmospheric and Environmental Sciences [Frankfurt/Main]
- 4. TROPOS - Leibniz Institute for Tropospheric Research
- 5. Institut für Ionenphysik und Angewandte Physik - Institute for Ion Physics and Applied Physics [Innsbruck]
- 6. UiO - University of Oslo

## Archive ouverte HAL – Anyons on the sphere: analytic states and spectrum

### Stephane Ouvry

^{1}Alexios P. Polychronakos#### Stephane Ouvry, Alexios P. Polychronakos. Anyons on the sphere: analytic states and spectrum.

*Nucl.Phys.B*, 2019, 949, pp.114797. ⟨10.1016/j.nuclphysb.2019.114797⟩. ⟨hal-02303026⟩We analyze the quantum mechanics of anyons on the sphere in the presence of a constant magnetic field. We introduce an operator method for diagonalizing the Hamiltonian and derive a set of exact anyon energy eigenstates, in partial correspondence with the known exact eigenstates on the plane. We also comment on possible connections of this system with integrable systems of the Calogero type.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Anyonic tight-binding models of parafermions and of fractionalized fermions

### Davide RossiniMatteo CarregaMarcello Calvanese StrinatiLeonardo Mazza

^{1}*Phys.Rev.B*, 2019, 99 (8), pp.085113. 〈10.1103/PhysRevB.99.085113〉Parafermions are emergent quasiparticles which generalize Majorana fermions and possess intriguing anyonic properties. The theoretical investigation of effective models hosting them is gaining considerable importance in view of present-day condensed-matter realizations where they have been predicted to appear. Here we study the simplest number-conserving model of particlelike Fock parafermions, namely a one-dimensional tight-binding model. By means of numerical simulations based on exact diagonalization and on the density-matrix renormalization group, we prove that this quadratic model is nonintegrable and displays bound states in the spectrum due to its peculiar anyonic properties. Moreover, we discuss its many-body physics, characterizing anyonic correlation functions and discussing the underlying Luttinger-liquid theory at low energies. In the case when Fock parafermions behave as fractionalized fermions, we are able to unveil interesting similarities with two counterpropagating edge modes of two neighboring Laughlin states at filling 1/3.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Anderson-like localization transition of random walks with resetting

### Denis Boyer

^{1}Andrea Falcón-Cortés^{2}Luca Giuggioli^{3}Satya N. Majumdar^{4}Satya Majumdar^{4}#### Denis Boyer, Andrea Falcón-Cortés, Luca Giuggioli, Satya N. Majumdar, Satya Majumdar. Anderson-like localization transition of random walks with resetting.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (5), pp.053204. ⟨10.1088/1742-5468/ab16c2⟩. ⟨hal-02291906⟩We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized phase settles above a critical resetting rate, or rate of memory use, and the probability density asymptotically adopts in this regime a non-equilibrium steady state similar to that of the well known problem of diffusion with resetting to the origin. The transition occurs because of the presence of a single impurity site where the resetting rate is lower than on other sites, and around which the walker spontaneously localizes. Near criticality, the localization length diverges with a critical exponent that falls in the same class as the self-consistent theory of Anderson localization of waves in random media. The critical dimensions are also the same in both problems. Our study provides analytically tractable examples of localization transitions in path-dependent, reinforced stochastic processes, which can be also useful for understanding spatial learning by living organisms.

- 1. Instituto de Fisica
- 2. UNAM - Universidad Nacional Autónoma de México
- 3. University of Bristol [Bristol]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Actin dynamics drive cell-like membrane deformation

### Camille Simon

^{1}Rémy KustersValentina Caorsi^{2}Antoine AllardMajdouline Abou-Ghali^{3}John Manzi^{3}Aurelie Di Cicco^{3}Daniel Lévy^{4}Martin Lenz^{5}Jean-Francois Joanny^{3}Clément Campillo^{6}Julie Plastino^{3}Pierre Sens^{3}Cécile Sykes^{7}#### Camille Simon, Rémy Kusters, Valentina Caorsi, Antoine Allard, Majdouline Abou-Ghali, et al.. Actin dynamics drive cell-like membrane deformation.

*Nature Physics*, Nature Publishing Group, 2019, 15 (6), pp.602-609. ⟨10.1038/s41567-019-0464-1⟩. ⟨hal-02148264⟩Cell membrane deformations are crucial for proper cell function. Specialized protein assemblies initiate inward or outward membrane deformations that the cell uses respectively to uptake external substances or probe the environment. The assembly and dynamics of the actin cytoskeleton are involved in this process, although their detailed role remains controversial. We show here that a dynamic, branched actin network is sufficient to initiate both inward and outward membrane deformation. The polymerization of a dense actin network at the membrane of liposomes produces inward membrane bending at low tension , while outward deformations are robustly generated regardless of tension. Our results shed light on the mechanism cells use to internalize material , both in mammalian cells, where actin polymerization forces are required when membrane tension is increased, and in yeast, where those forces are necessary to overcome the opposing turgor pressure. By combining experimental observations with physical modelling, we propose a mechanism that explains how membrane tension and the architecture of the actin network regulate cell-like membrane deformations.

- 1. LPS - Laboratoire de Psychologie Sociale
- 2. INSP - Institut des Nanosciences de Paris
- 3. PCC - Physico-Chimie-Curie
- 4. Chercheur indépendant
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LAMBE - UMR 8587 - Laboratoire Analyse et Modélisation pour la Biologie et l'Environnement
- 7. UPMC - Université Pierre et Marie Curie - Paris 6

## Archive ouverte HAL – A super-resolution platform for correlative live single-molecule imaging and STED microscopy

### V. InavalliMartin Lenz

^{1}Corey Butler^{2}Julie Angibaud^{3}Benjamin Compans^{4}Florian Levet^{5}Jan TønnesenOlivier Rossier^{2}Gregory Giannone^{2}Olivier Thoumine^{6}Eric Hosy^{2}Daniel Choquet^{6}Jean-Baptiste Sibarita^{2}U. Valentin Nägerl^{2}#### V. Inavalli, Martin Lenz, Corey Butler, Julie Angibaud, Benjamin Compans, et al.. A super-resolution platform for correlative live single-molecule imaging and STED microscopy.

*Nature Methods*, Nature Publishing Group, 2019, ⟨10.1038/s41592-019-0611-8⟩. ⟨hal-02348164⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IINS - Interdisciplinary Institute for Neuroscience
- 3. U1064 Inserm - CRTI - Centre de Recherche en Transplantation et Immunologie
- 4. Interdisciplinary Institute for Neuroscience
- 5. LaBRI - Laboratoire Bordelais de Recherche en Informatique
- 6. PCS - Physiologie cellulaire de la synapse

## Archive ouverte HAL – A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle

### Giacomo Gradenigo

^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}#### Giacomo Gradenigo, Satya N. Majumdar, Satya Majumdar. A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (5), pp.053206. ⟨10.1088/1742-5468/ab11be⟩. ⟨hal-02291859⟩We study the probability distribution $P(X_N=X,N)$ of the total displacement $X_N$ of an $N$-step run and tumble particle on a line, in presence of a constant nonzero drive $E$. While the central limit theorem predicts a standard Gaussian form for $P(X,N)$ near its peak, we show that for large positive and negative $X$, the distribution exhibits anomalous large deviation forms. For large positive $X$, the associated rate function is nonanalytic at a critical value of the scaled distance from the peak where its first derivative is discontinuous. This signals a first-order dynamical phase transition from a homogeneous `fluid' phase to a `condensed' phase that is dominated by a single large run. A similar first-order transition occurs for negative large fluctuations as well. Numerical simulations are in excellent agreement with our analytical predictions.

- 1. LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – A consistent quadratic curvature-tilt theory for fluid lipid membranes

### M. Mert Terzi

^{1}Muhammed Ergüder^{2}Markus Deserno^{2}#### M. Mert Terzi, Muhammed Ergüder, Markus Deserno. A consistent quadratic curvature-tilt theory for fluid lipid membranes.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 151 (16), pp.164108. ⟨10.1063/1.5119683⟩. ⟨hal-02512290⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CMU - Carnegie Mellon University [Pittsburgh]

## Archive ouverte HAL – 4 π and 8 π dual Josephson effects induced by symmetry defects

### Corneliu Malciu

^{1}Leonardo Mazza^{2}Christophe Mora^{1}#### Corneliu Malciu, Leonardo Mazza, Christophe Mora. 4 π and 8 π dual Josephson effects induced by symmetry defects.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 99 (12), ⟨10.1103/PhysRevB.99.125153⟩. ⟨hal-02102139⟩In topological insulator edges, the duality between the Zeeman field orientation and the proximitized superconducting phase has been recently exploited to predict a magneto-Josephson effect with a 4$\pi$ periodicity. We revisit this latter Josephson effect in the light of this duality and show that the same 4$\pi$ quantum anomaly occurs when bridging two spinless Thouless pumps to a p-wave superconducting region that could be as small as a single and experimentally-relevant superconducting quantum dot - a point-like defect. This interpretation as a dual Josephson effect never requires the presence of Majorana modes but rather builds on the topological properties of adiabatic quantum pumps with Z topological invariants. It allows for the systematic construction of dual Josephson effects of arbitrary periodicity, such as 4$\pi$ and 8$\pi$, by using point-like defects whose symmetry differs from that of the pump, dubbed symmetry defects. Although adiabatic quantum pumps are typically discussed via mappings to two-dimensional geometries, we show that this phenomenology does not have any counterpart in conventional two-dimensional systems.

- 1. LPA - Laboratoire Pierre Aigrain
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## A consistent quadratic curvature-tilt theory for fluid lipid membranes – Archive ouverte HAL

### M. Mert Terzi

^{1}Muhammed Ergüder^{2}Markus Deserno^{2}#### M. Mert Terzi, Muhammed Ergüder, Markus Deserno. A consistent quadratic curvature-tilt theory for fluid lipid membranes.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 151 (16), pp.164108. ⟨10.1063/1.5119683⟩. ⟨hal-02512290⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CMU - Carnegie Mellon University [Pittsburgh]

## Towards Quantum Simulation with Circular Rydberg Atoms

### Thanh Long Nguyen

^{1}Jean-Michel Raimond^{1}Clément Sayrin^{1}Rodrigo Cortinas^{1}Tigrane Cantat-Moltrecht^{1}Fédéric Assemat^{1}Igor Dotsenko^{1}Sébastien Gleyzes^{1}Serge Haroche^{1}Guillaume Roux^{2}Thierry Jolicoeur^{2}Michel Brune^{1}*Physical Review X*, American Physical Society, 2018, 8 (1), 〈10.1103/PhysRevX.8.011032〉The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation.

- 1. LKB [Collège de France] - Laboratoire Kastler Brossel
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Topological Zak Phase in Strongly-Coupled LC Circuits

### Tal Goren

^{1}Kirill Plekhanov^{1, 2}Félicien Appas^{1}Karyn Le Hur^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\cal Z}_2$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sub-lattice symmetry, represented by an anti-unitary transformation. We present a methos to measure the winding of the topological Zak phase across the Brillouin zone by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems. We study the robustness of edge modes towards disorder.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The impact of the injection protocol on an impurity’s stationary state

### Oleksandr Gamayun

^{1, 2}Oleg Lychkovskiy^{3, 4, 5}Evgeni Burovski^{6, 7}Matthew Malcomson^{8}Vadim V. Cheianov^{1}Mikhail B. Zvonarev^{9}*Physical Review Letters*, American Physical Society, 2018We examine stationary state properties of an impurity particle injected into a one-dimensional quantum gas. We show that the value of the impurity's end velocity lies between zero and the speed of sound in the gas, and is determined by the injection protocol. This way, the impurity's constant motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of Landau approach to superfluidity. We provide exact analytic results in the thermodynamic limit, and perform finite-size numerical simulations to demonstrate that the predicted phenomena are within the reach of the existing ultracold gases experiments.

- 1. Universiteit Leiden [Leiden]
- 2. Bogolyubov Institute for Theoretical Physics
- 3. Skoltech - Skolkovo Institute of Science and Technology [Moscow]
- 4. Steklov Mathematical Institute of Russian Academy of Sciences
- 5. Russian Quantum Center
- 6. National Research University Higher School of Economics [Moscow]
- 7. Science Center in Chernogolovka
- 8. Lancaster University
- 9. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Surface temperatures in New York City: Geospatial data enables the accurate prediction of radiative heat transfer

### Masoud Ghandehari

^{1}Thorsten Emig^{2, 3}Milad Aghamohamadnia^{1}*Scientific Reports*, Nature Publishing Group, 2018Three decades into the research seeking to derive the urban energy budget, the dynamics of the thermal exchange between the densely built infrastructure and the environment are still not well understood. We present a novel hybrid experimental-numerical approach for the analysis of the radiative heat transfer in New York City. The aim of this work is to contribute to the calculation of the urban energy budget, in particular the stored energy. Improved understanding of urban thermodynamics incorporating the interaction of the various bodies will have implications on energy conservation at the building scale, as well as human health and comfort at the urban scale. The platform presented is based on longwave hyperspectral imaging of nearly 100 blocks of Manhattan, and a geospatial radiosity model that describes the collective radiative heat exchange between multiple buildings. The close comparison of temperature values derived from measurements and the computed surface temperatures (including streets and roads) implies that this geospatial, thermodynamic numerical model applied to urban structures, is promising for accurate and high resolution analysis of urban surface temperatures.

- 1. NYU Tandon School of Engineering
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MSE2 - Multiscale Materials Science for Energy and Environment

## Superfluidity of identical fermions in an optical lattice: Atoms and polar molecules

### A. K. Fedorov

^{1}V. I. Yudson^{2}G. V. Shlyapnikov^{3, 4, 1}*AIP Conference Proceedings*, American Institute of Physics, 2018, 〈10.1063/1.5025460〉In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.

- 1. Russian Quantum Center
- 2. Institute of Spectroscopy
- 3. Wuhan Institute of Physics and Mathematics
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases

### L. Samaj

^{1}M. Trulsson^{2}E. Trizac^{3}*Soft Matter*, Royal Society of Chemistry, 2018We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner Strong-Coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of $d$ comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.

- 1. Institute of Physics
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

### Kanaya Malakar

^{1}V. Jemseena^{2}Anupam Kundu^{2}K. Vijay Kumar^{2}Sanjib Sabhapandit^{3}Satya N. Majumdar^{4}S. Redner^{5}Abhishek Dhar^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2018We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.

- 1. Presidency University
- 2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 3. Raman Research Institute
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Santa Fe Institute

## Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?

### Xiangyu Cao

^{1, 2}Alexandre Nicolas^{1}Denny Trimcev^{1, 3}Alberto Rosso^{1}*Soft Matter*, Royal Society of Chemistry, 2018, 14 (18), pp.3640 - 3651. 〈10.1039/C7SM02510F〉The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like `impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of California [Berkeley]
- 3. ENS Paris - École normale supérieure - Paris

## Singularities of Floquet scattering and tunneling

### H. Landa

^{1, 2}*Physical Review A*, American Physical Society, 2018, 97 (4), 〈10.1103/PhysRevA.97.042705〉We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive amplitude, making the S-matrix nonanalytic at a singular point. For the corresponding quasi-bound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low energy (s-wave) particles and their conversion to high energy outgoing (mostly p-) waves. We examine the relation of such Floquet singularities, lacking in an effective time independent approximation, with well known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power law forces and subject to periodic fields, e.g. co-trapped ions and atoms.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Role of City Texture in Urban Heat Islands at Nighttime

### J.M. SobstylT. Emig

^{1}M.J. QomiF.-J. UlmR.J.-M. Pellenq*Physical Review Letters*, American Physical Society, 2018, 120 (10), pp.108701. 〈10.1103/PhysRevLett.120.108701〉An urban heat island (UHI) is a climate phenomenon that results in an increased air temperature in cities when compared to their rural surroundings. In this Letter, the dependence of an UHI on urban geometry is studied. Multiyear urban-rural temperature differences and building footprints data combined with a heat radiation scaling model are used to demonstrate for more than 50 cities worldwide that city texture—measured by a building distribution function and the sky view factor—explains city-to-city variations in nocturnal UHIs. Our results show a strong correlation between nocturnal UHIs and the city texture.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience – Archive ouverte HAL

### Silvia Grigolon

^{1}Barbara Bravi^{2}Olivier C. Martin^{1, 3}#### Silvia Grigolon, Barbara Bravi, Olivier C. Martin. Responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience.

*Royal Society Open Science*, The Royal Society, 2018, 5 (1), pp.1-15. ⟨10.1098/rsos.172098⟩. ⟨hal-01735356⟩Plants depend on the signaling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signaling network involves a negative feedback at the level of the Aux/IAA proteins which mediate the influence of auxin (the signal) on the ARF transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signaling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative regulatory feedback loop allows the system to have a far larger sensitivity in its dynamical response to auxin. At the same time, this sensitivity does not prevent the system from being highly resilient. Given this insight, we reconsider previously published models and build a new quantitative and calibrated biomolecular model of auxin signaling.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. King‘s College London
- 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)

## Responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience

### Silvia Grigolon

^{1}Barbara Bravi^{2}Olivier C. Martin^{1, 3}*Royal Society Open Science*, The Royal Society, 2018, 5 (1), 〈10.1098/rsos.172098〉Plants depend on the signaling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signaling network involves a negative feedback at the level of the Aux/IAA proteins which mediate the influence of auxin (the signal) on the ARF transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signaling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative regulatory feedback loop allows the system to have a far larger sensitivity in its dynamical response to auxin. At the same time, this sensitivity does not prevent the system from being highly resilient. Given this insight, we reconsider previously published models and build a new quantitative and calibrated biomolecular model of auxin signaling.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. King‘s College London [London]
- 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)

## Planar screening by charge polydisperse counterions

### M. Trulsson

^{1, 2}E. Trizac^{1}L. Samaj^{3}*Journal of Physics: Condensed Matter*, IOP Publishing, 2018, 30 (3), 〈10.1088/1361-648X/aa9a79〉We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane plate, when the counterions are characterised by a distribution of charges (or valence), $n(q)$. We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions $n(q)$, for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous $n(q)$ behaviour is already featured by discrete mixtures with a relatively small number of constituents.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Lund University [Lund]
- 3. Institute of Physics

## Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

### Xiangyu Cao

^{1}Vincent Démery^{2, 3}Alberto Rosso^{4, 5}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (23), 〈10.1088/1751-8121/aac02f〉The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility ${\mu}_{\text{eff}}$ . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force $f_c$. At small disorder, we unveil an intermediary linear regime for $f_c < f < 1$ characterized by the renormalized mobility ${\mu}_{\text{eff}}$. Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

- 1. University of California [Berkeley]
- 2. ESPCI - UMR Gulliver
- 3. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. KITP - Kavli Institute for Theoretical Physics

## Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions

### V. Roberdel

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1, 3}*Physical Review A*, American Physical Society, 2018, 97 (5), 〈10.1103/PhysRevA.97.053419〉We present a comprehensive phase-space treatment of the motion of charged particles in electrodynamic traps. Focusing on five-wire surface-electrode Paul traps, we study the details of integrable and chaotic motion of a single ion. We introduce appropriate phase-space measures and give a universal characterization of the trap effectiveness as a function of the parameters. We rigorously derive the commonly used (time-independent) pseudopotential approximation, quantify its regime of validity and analyze the mechanism of its breakdown within the time-dependent potential. The phase space approach that we develop gives a general framework for describing ion dynamics in a broad variety of surface Paul traps. To probe this framework experimentally, we propose and analyze, using numerical simulations, an experiment that can be realized with an existing four-wire trap. We predict a robust experimental signature of the existence of trapping pockets within a mixed regular and chaotic phase-space structure. Intricately rich escape dynamics suggest that surface traps give access to exploring microscopic Hamiltonian transport phenomena in phase space.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technologies
- 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Origin of the correlations between exit times in pedestrian flows through a bottleneck

### Alexandre Nicolas

^{1}Ioannis Touloupas^{1}*Journal of Statistical Mechanics*, 2018, 1, pp.013402. 〈http://iopscience.iop.org/article/10.1088/1742-5468/aa9dcd〉Robust statistical features have emerged from the microscopic analysis of dense pedestrian flows through a bottleneck, notably with respect to the time gaps between successive passages. We pinpoint the mechanisms at the origin of these features thanks to simple models that we develop and analyse quantitatively. We disprove the idea that anticorrelations between successive time gaps (i.e., an alternation between shorter ones and longer ones) are a hallmark of a zipper-like intercalation of pedestrian lines and show that they simply result from the possibility that pedestrians from distinct 'lines' or directions cross the bottleneck within a short time interval. A second feature concerns the bursts of escapes, i.e., egresses that come in fast succession. Despite the ubiquity of exponential distributions of burst sizes, entailed by a Poisson process, we argue that anomalous (power-law) statistics arise if the bottleneck is nearly congested, albeit only in a tiny portion of parameter space. The generality of the proposed mechanisms implies that similar statistical features should also be observed for other types of particulate flows.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models

### Xiangyu CaoPierre Le Doussal

^{1}Alberto Rosso^{2}Raoul Santachiara^{2}*Phys.Rev.E*, 2018, 97 (4), pp.042111. 〈10.1103/PhysRevE.97.042111〉We study transitions in log-correlated random energy models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a., pre-freezing). By means of LFT-logREM mapping, replica symmetry breaking and traveling-wave equation techniques, we unify both transitions in a two-parameter diagram, which describes the free-energy large deviations of logREMs with a deterministic background log potential, or equivalently, the joint moments of the free energy and Gibbs measure in logREMs without background potential. Under the LFT-logREM mapping, the transitions correspond to the competition of discrete and continuous terms in a four-point correlation function. Our results provide a statistical interpretation of a peculiar nonlocality of the operator product expansion in LFT. The results are rederived by a traveling-wave equation calculation, which shows that the features of LFT responsible for the transitions are reproduced in a simple model of diffusion with absorption. We examine also the problem by a replica symmetry breaking analysis. It complements the previous methods and reveals a rich large deviation structure of the free energy of logREMs with a deterministic background log potential. Many results are verified in the integrable circular logREM, by a replica-Coulomb gas integral approach. The related problem of common length (overlap) distribution is also considered. We provide a traveling-wave equation derivation of the LFT predictions announced in a precedent work.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## On characteristic polynomials for a generalized chiral random matrix ensemble with a source

### Yan FyodorovJacek Grela

^{1}Eugene Strahov*J.Phys.A*, 2018, 51 (13), pp.134003. 〈10.1088/1751-8121/aaae2a〉We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

### Christophe Texier

^{1, 2}Johannes Mitscherling^{1, 3}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 〈10.02214〉We study the non-linear conductance $\mathcal{G}\sim\partial^2I/\partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim0.006\,E_\mathrm{Th}^{-1}$ (and $\langle\mathcal{G}\rangle=0$), where $E_\mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $\mathcal{G}_a\sim0.001\,(gE_\mathrm{Th})^{-1}$, where $g\gg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_\varphi\ll L$, where $L_\varphi$ is the phase coherence length, we get $\mathcal{G}\sim(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$, and $\mathcal{G}_a\sim(L_\varphi/L)^{11/2}(gE_\mathrm{Th})^{-1}\ll\mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_\varphi\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim(L_T/L)(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $\mathcal{G}_a\sim(L_T/L)^2(L_\varphi/L)^{7/2}(gE_\mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides
- 3. Max Planck Institute for Solid State Research

## Negative Differential Mobility in Interacting Particle Systems

### Amit Kumar Chatterjee

^{1}Urna Basu^{2}P. K. Mohanty^{1}*Physical Review E*, American Physical Society (APS), 2018Driven particles in presence of crowded environment, obstacles or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. We propose a new mechanism for complex many-particle systems where slowing down of certain {\it non-driven} degrees of freedom by the external field can give rise to NDM. This phenomenon, resulting from inter-particle interactions, is illustrated in a pedagogical example of two interacting random walkers, one of which is biased by an external field while the same field only slows down the other keeping it unbiased. We also introduce and solve exactly the steady state of several driven diffusive systems, including a two species exclusion model, asymmetric misanthrope and zero-range processes, to show explicitly that this mechanism indeed leads to NDM.

- 1. Saha Institute of Nuclear Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Momentum correlations as signature of sonic Hawking radiation in Bose-Einstein condensates

### A. Fabbri

^{1}N. Pavloff^{2}*SciPost Phys.*, 2018, 4, pp.019. 〈10.21468/SciPostPhys.4.4.019〉We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quenches.

- 1. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Modeling of networks and globules of charged domain walls observed in pump and pulse induced states

### Petr Karpov

^{1}Serguei Brazovskii^{2, 1, 3}*Scientific Reports*, Nature Publishing Group, 2018Experiments on optical and STM injection of carriers in layered $\mathrm{MX_2}$ materials revealed the formation of nanoscale patterns with networks and globules of domain walls. This is thought to be responsible for the metallization transition of the Mott insulator and for stabilization of a "hidden" state. In response, here we present studies of the classical charged lattice gas model emulating the superlattice of polarons ubiquitous to the material of choice $1T-\mathrm{TaS_2}$. The injection pulse was simulated by introducing a small random concentration of voids which subsequent evolution was followed by means of Monte Carlo cooling. Below the detected phase transition, the voids gradually coalesce into domain walls forming locally connected globules and then the global network leading to a mosaic fragmentation into domains with different degenerate ground states. The obtained patterns closely resemble the experimental STM visualizations. The surprising aggregation of charged voids is understood by fractionalization of their charges across the walls' lines.

- 1. MISIS - National University of Science and Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IJS - Jozef Stefan Institute [Ljubljana, Slovenia]

## Matrix product state description of Halperin states

### V. Crépel

^{1}B. Estienne^{2}B.A. Bernevig^{1, 3}P. Lecheminant^{4}N. Regnault^{1}*Phys.Rev.B*, 2018, 97 (16), pp.165136. 〈10.1103/PhysRevB.97.165136〉Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.

- 1. LPA - Laboratoire Pierre Aigrain
- 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. LPTM - Laboratoire de Physique Théorique et Modélisation

## Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

### Thomas Barthel

^{1, 2}Caterina De Bacco^{2, 3}Silvio Franz^{2}*Physical Review E*, American Physical Society (APS), 2018, 97 (1), 〈10.1103/PhysRevE.97.010104〉We introduce and apply a novel efficient method for the precise simulation of stochastic dynamical processes on locally tree-like graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, the new approach is based on a matrix product approximation of the so-called edge messages -- conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both, single instances as well as the thermodynamic limit. We employ it to examine prototypical non-equilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

- 1. Duke university [Durham]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Santa Fe Institute

## Log-correlated random-energy models with extensive free-energy fluctuations: Pathologies caused by rare events as signatures of phase transitions

### Xiangyu Cao

^{1}Yan FyodorovPierre Le Doussal^{2}*Phys.Rev.E*, 2018, 97 (2), pp.022117. 〈10.1103/PhysRevE.97.022117〉We address systematically an apparent nonphysical behavior of the free-energy moment generating function for several instances of the logarithmically correlated models: the fractional Brownian motion with Hurst index H=0 (fBm0) (and its bridge version), a one-dimensional model appearing in decaying Burgers turbulence with log-correlated initial conditions and, finally, the two-dimensional log-correlated random-energy model (logREM) introduced in Cao et al. [Phys. Rev. Lett. 118, 090601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.090601] based on the two-dimensional Gaussian free field with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly nonphysical vanishing of the moment generating function for some values of parameters is related to the termination point transition (i.e., prefreezing). We study the associated universal log corrections in the frozen phase, both for logREMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the nontrivial free-energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Localization of soft modes at the depinning transition

### Xiangyu Cao

^{1}Sebastián Bouzat^{2}Alejandro B. Kolton^{2}Alberto Rosso^{1}*Physical Review E*, American Physical Society (APS), 2018, 97 (2), 〈10.1103/PhysRevE.97.022118〉We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead very similar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter of avalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection between its localization length and the Larkin length of the depinning model. In the fully connected model, the weak--strong pinning transition coincides with a peculiar localization transition of the ground state.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centro Atómico Bariloche [Argentine]

## Liquid beyond the van der Waals paradigm

### Dmitry Petrov

^{1}*Nature Physics*, Nature Publishing Group, 2018, 14 (3), pp.211 - 212. 〈10.1038/s41567-018-0052-9〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Like-charge attraction in a one-dimensional setting: the importance of being odd

### E. Trizac

^{1}G. Tellez^{2}*European Journal of Physics*, European Physical Society, 2018From cement cohesion to DNA condensation, a proper statistical physics treatment of systems with long range forces is important for a number of applications in physics, chemistry, and biology. We compute here the effective force between fixed charged macromolecules, screened by oppositely charged mobile ions (counterions). We treat the problem in a one dimensional configuration, that allows for interesting discussion and derivation of exact results, remaining at a level of mathematical difficulty compatible with an undergraduate course. Emphasis is put on the counter-intuitive but fundamental phenomenon of like-charge attraction, that our treatment brings for the first time to the level of undergraduate teaching. The parity of the number of counterions is shown to play a prominent role, which sheds light on the binding mechanism at work when like-charge macromolecules do attract.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departamento de Fisica

## Higher-order corrections to the effective potential close to the jamming transition in the perceptron model

### Ada Altieri

^{1, 2}*Physical Review E*, American Physical Society (APS), 2018, 97 (1), 〈10.1103/PhysRevE.97.012103〉We analyze the perceptron model performing a Plefka-like expansion of the free energy. This model falls in the same universality class as hard spheres near jamming, allowing to get exact predictions in high dimensions for more complex systems. Our method enables to define an effective potential (or TAP free energy), namely a coarse-grained functional depending on the contact forces and the effective gaps between the particles. The derivation is performed up to the third order, with a particular emphasis on the role of third order corrections to the TAP free energy. These corrections, irrelevant in a mean-field framework in the thermodynamic limit, might instead play a fundamental role when considering finite-size effects. We also study the typical behavior of the forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. In our analysis, third order contributions vanish in the jamming limit, both for the potential and the generalized forces, in agreement with the argument proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the scalings emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.

- 1. Department of Physics [Roma La Sapienza]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## High-precision simulation of the height distribution for the KPZ equation

### Alexander K. Hartmann

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Alberto Rosso^{3}Gregory Schehr^{3}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2018, 121 (6), 〈10.1209/0295-5075/121/67004〉The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10^{-1000} in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2 respectively, are preserved until large time. We present some evidence for the predicted non-trivial crossover in the left tail from the 5/2 tail exponent to the cubic tail of Tracy-Widom, although the details of the full scaling form remains beyond reach.

- 1. University of Oldenburg
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Fluctuations of observables for free fermions in a harmonic trap at finite temperature

### Aurélien Grabsch

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}Christophe Texier^{1}*SciPost Physics Journals*, the SciPost Foundation, 2018We study a system of 1D noninteracting spinless fermions in a confining trap at finite temperature. We first derive a useful and general relation for the fluctuations of the occupation numbers valid for arbitrary confining trap, as well as for both canonical and grand canonical ensembles. Using this relation, we obtain compact expressions, in the case of the harmonic trap, for the variance of certain observables of the form of sums of a function of the fermions' positions, $\mathcal{L}=\sum_n h(x_n)$. Such observables are also called linear statistics of the positions. As anticipated, we demonstrate explicitly that these fluctuations do depend on the ensemble in the thermodynamic limit, as opposed to averaged quantities, which are ensemble independent. We have applied our general formalism to compute the fluctuations of the number of fermions $\mathcal{N}_+$ on the positive axis at finite temperature. Our analytical results are compared to numerical simulations. We discuss the universality of the results with respect to the nature of the confinement.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Extremes of $2d$ Coulomb gas: universal intermediate deviation regime

### Bertrand Lacroix-A-Chez-Toine

^{1}Aurélien Grabsch^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018, 〈10.06222〉In this paper, we study the extreme statistics in the complex Ginibre ensemble of $N \times N$ random matrices with complex Gaussian entries, but with no other symmetries. All the $N$ eigenvalues are complex random variables and their joint distribution can be interpreted as a $2d$ Coulomb gas with a logarithmic repulsion between any pair of particles and in presence of a confining harmonic potential $v(r) \propto r^2$. We study the statistics of the eigenvalue with the largest modulus $r_{\max}$ in the complex plane. The typical and large fluctuations of $r_{\max}$ around its mean had been studied before, and they match smoothly to the right of the mean. However, it remained a puzzle to understand why the large and typical fluctuations to the left of the mean did not match. In this paper, we show that there is indeed an intermediate fluctuation regime that interpolates smoothly between the large and the typical fluctuations to the left of the mean. Moreover, we compute explicitly this "intermediate deviation function" (IDF) and show that it is universal, i.e. independent of the confining potential $v(r)$ as long as it is spherically symmetric and increases faster than $\ln r^2$ for large $r$ with an unbounded support. If the confining potential $v(r)$ has a finite support, i.e. becomes infinite beyond a finite radius, we show via explicit computation that the corresponding IDF is different. Interestingly, in the borderline case where the confining potential grows very slowly as $v(r) \sim \ln r^2$ for $r \gg 1$ with an unbounded support, the intermediate regime disappears and there is a smooth matching between the central part and the left large deviation regime.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Energy of N two-dimensional bosons with zero-range interactions

### Betzalel Bazak

^{1}Dmitry S. Petrov^{2}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2018, 20 (2), 〈10.1088/1367-2630/aaa64f〉We derive an integral equation describing $N$ two-dimensional bosons with zero-range interactions and solve it for the ground state energy $B_N$ by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go beyond the scaling $B_N\propto 8.567^N$ predicted by Hammer and Son [Phys. Rev. Lett. {\bf 93}, 250408 (2004)] in the large-$N$ limit.

- 1. IPNO - Institut de Physique Nucléaire d'Orsay
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model

### Kirill Plekhanov

^{1, 2}Ivana Vasić^{3}Alexandru Petrescu^{4}Rajbir Nirwan^{5}Guillaume Roux^{2}Walter Hofstetter^{5}Karyn Le Hur^{1}*Physical Review Letters*, American Physical Society, 2018, 120 (15), 〈10.1103/PhysRevLett.120.157201〉Recently, the frustrated XY model for spins-1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultra-cold atoms setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using the bosonic dynamical mean-field theory. Focussing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institute of Physics [Belgrade]
- 4. EE - Department of Electrical Engineering [Princeton]
- 5. ITP - Institut für Theoretische Physik [Frankfurt am Main]

## Eigenstate versus Zeeman-based approaches to the solid effect

### Inés Rodríguez-Arias

^{1}Alberto Rosso^{1}Andrea De Luca^{2}*Magnetic Resonance in Chemistry*, Wiley, 2018, 56 (7), pp.689 - 698. 〈10.1002/mrc.4724〉The solid effect is one of the simplest and most effective mechanisms for Dynamic Nuclear Polarization. It involves the exchange of polarization between one electron and one nuclear spin coupled via the hyperfine interaction. Even for such a small spin system, the theoretical understanding is complicated by the contact with the lattice and the microwave irradiation. Both being weak, they can be treated within perturbation theory. In this work, we analyze the two most popular perturbation schemes: the Zeeman and the eigenstate-based approaches which differ in the way the hyperfine interaction is treated. For both schemes, we derive from first principles an effective Liouville equation which describes the density matrix of the spin system; we then study numerically the behavior of the nuclear polarization for several values of the hyperfine coupling. In general, we obtain that the Zeeman-based approach underestimates the value of the nuclear polarization. By performing a projection onto the diagonal part of the spin-system density matrix, we are able to understand the origin of the discrepancy, which is due to the presence of parasite leakage transitions appearing whenever the Zeeman basis is employed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Rudolf Peierls Centre for Theoretical Physics

## Duality in Power-Law Localization in Disordered One-Dimensional Systems

### X. Deng

^{1}V. e. Kravtsov^{2, 3}G. v. Shlyapnikov^{4, 5, 6, 7, 8}L. Santos^{1}*Physical Review Letters*, American Physical Society, 2018, 120 (11), 〈10.1103/PhysRevLett.120.110602〉The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, $1/r^a$. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of $a>0$. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops ($a<1$) and short-range hops ($a>1$) in which the wave function amplitude falls off algebraically with the same power $\gamma$ from the localization center.

- 1. LUH - Leibniz Universität Hannover [Hannover]
- 2. ICTP - International Center for Theoretical Physics [Trieste]
- 3. L.D. Landau Institute for Theoretical Physics of RAS
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. SPEC - UMR3680 - Service de physique de l'état condensé
- 6. Russian Quantum Center
- 7. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 8. Wuhan Institute of Physics and Mathematics

## Deformation and flow of amorphous solids: Insights from elastoplastic models – Archive ouverte HAL

### Alexandre Nicolas

^{1}Ezequiel E. Ferrero^{2}Kirsten Martens^{3}Jean-Louis Barrat^{3}#### Alexandre Nicolas, Ezequiel E. Ferrero, Kirsten Martens, Jean-Louis Barrat. Deformation and flow of amorphous solids: Insights from elastoplastic models.

*Reviews of Modern Physics*, American Physical Society, 2018, 90 (4), ⟨10.1103/RevModPhys.90.045006⟩. ⟨hal-02919245⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centro Atómico Bariloche [Argentine]
- 3. LIPhy [2020-….] - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] [2020-….]

## Correlations of occupation numbers in the canonical ensemble and application to a Bose-Einstein condensate in a one-dimensional harmonic trap

### Olivier Giraud

^{1}Aurélien Grabsch^{1}Christophe Texier^{1}*Physical Review A*, American Physical Society, 2018, 97 (5), 〈10.1103/PhysRevA.97.053615〉We study statistical properties of $N$ non-interacting identical bosons or fermions in the canonical ensemble. We derive several general representations for the $p$-point correlation function of occupation numbers $\overline{n_1\cdots n_p}$. We demonstrate that it can be expressed as a ratio of two $p\times p$ determinants involving the (canonical) mean occupations $\overline{n_1}$, ..., $\overline{n_p}$, which can themselves be conveniently expressed in terms of the $k$-body partition functions (with $k\leq N$). We draw some connection with the theory of symmetric functions, and obtain an expression of the correlation function in terms of Schur functions. Our findings are illustrated by revisiting the problem of Bose-Einstein condensation in a 1D harmonic trap, for which we get analytical results. We get the moments of the occupation numbers and the correlation between ground state and excited state occupancies. In the temperature regime dominated by quantum correlations, the distribution of the ground state occupancy is shown to be a truncated Gumbel law. The Gumbel law, describing extreme value statistics, is obtained when the temperature is much smaller than the Bose-Einstein temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Closed-Loop Estimation of Retinal Network Sensitivity by Local Empirical Linearization

### Ulisse Ferrari

^{1}Christophe Gardella^{1}Olivier Marre^{1}Thierry Mora^{2}*eNeuro*, Society for Neuroscience, 2018, 4 (6), pp.ENEURO.0166-17.2017. 〈10.1523/ENEURO.0166-17.2017〉Understanding how sensory systems process information depends crucially on identifying which features of the stimulus drive the response of sensory neurons, and which ones leave their response invariant. This task is made difficult by the many nonlinearities that shape sensory processing. Here, we present a novel perturbative approach to understand information processing by sensory neurons, where we linearize their collective response locally in stimulus space. We added small perturbations to reference stimuli and tested if they triggered visible changes in the responses, adapting their amplitude according to the previous responses with closed-loop experiments. We developed a local linear model that accurately predicts the sensitivity of the neural responses to these perturbations. Applying this approach to the rat retina, we estimated the optimal performance of a neural decoder and showed that the nonlinear sensitivity of the retina is consistent with an efficient encoding of stimulus information. Our approach can be used to characterize experimentally the sensitivity of neural systems to external stimuli locally, quantify experimentally the capacity of neural networks to encode sensory information, and relate their activity to behavior.

- 1. Institut de la Vision
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Cell contraction induces long-ranged stress stiffening in the extracellular matrix

### Yu Long Han

^{1}Pierre Ronceray^{2}Guoqiang Xu^{1}Andrea Malandrino^{3, 1}Roger Kamm^{1}Martin Lenz^{4}Chase P. Broedersz^{5}Ming Guo^{1}*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2018Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing Nonlinear Stress Inference Microscopy (NSIM), a novel technique to infer stress fields in a 3D matrix from nonlinear microrheology measurement with optical tweezers. Using NSIM and simulations, we reveal a long-ranged propagation of cell-generated stresses resulting from local filament buckling. This slow decay of stress gives rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which could form a mechanism for mechanical communication between cells.

- 1. MIT - Massachusetts Institute of Technology
- 2. Princeton Center for Theoretical Science
- 3. IBEC - Institute for Bioengineering of Catalonia [Barcelona]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Ludwig-Maximilians-Universität München

## Building blocks of topological quantum chemistry: Elementary band representations

### Jennifer Cano

^{1}Barry Bradlyn^{1}Zhijun Wang^{1}L. Elcoro^{2}M. G. Vergniory^{2}C. Felser^{3}M. I. Aroyo^{2}B. Andrei Bernevig^{4, 5, 6}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 97 (3), 〈10.1103/PhysRevB.97.035139〉The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of "elementary" band representations. In Nature 547, 298-305 (2017), we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here, we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time-reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wavefunctions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, which we introduced in Nature 547, 298-305 (2017), we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. University of the Basque Country - University of the Basque Country
- 3. Max Planck Institute for Chemical Physics of Solids
- 4. DPPU - Department of Physics,Princeton University
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LPA - Laboratoire Pierre Aigrain

## Band connectivity for topological quantum chemistry: Band structures as a graph theory problem

### Barry Bradlyn

^{1}L. Elcoro^{2}M. G. Vergniory^{2}Jennifer Cano^{1}Zhijun Wang^{1}C. Felser^{3}M. I. Aroyo^{2}B. Andrei Bernevig^{4, 5, 6}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 97 (3), 〈10.1103/PhysRevB.97.035138〉The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature 547, 298 (2017)], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local "k-dot-p" band structures across the Brillouin zone in terms of graph theory. In the current manuscript we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph-theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. University of the Basque Country - University of the Basque Country
- 3. Max Planck Institute for Chemical Physics of Solids
- 4. DPPU - Department of Physics,Princeton University
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

### Aurélien Grabsch

^{1}Dmitry V. SavinChristophe Texier^{1}*J.Phys.A*, 2018, 51 (40), pp.404001. 〈10.1088/1751-8121/aada43〉We consider wave propagation in a complex structure coupled to a finite number N of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the concept of time delays, related to the energy (or frequency) derivative of the scattering matrix . We develop a random matrix approach to study the statistical properties of the symmetrised Wigner–Smith time-delay matrix , and obtain the joint distribution of and for the system with non-ideal contacts, characterised by a finite transmission probability (per channel) . We derive two representations of the distribution of in terms of matrix integrals specified by the Dyson symmetry index (the general case of unequally coupled channels is also discussed). We apply this to the Wigner time delay , which is an important quantity providing the density of states of the open system. Using the obtained results, we determine the distribution of the Wigner time delay in the weak coupling limit and identify the following three regimes. (i) The large deviations at small times (measured in units of the Heisenberg time) are characterised by the limiting behaviour for . (ii) The distribution shows the universal behaviour in some intermediate range . (iii) It has a power law decay for large .

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Wigner function of noninteracting trapped fermions

### David Dean

^{1}Pierre Le Doussal^{2}Satya Majumdar^{3}Gregory Schehr^{3}*Physical Review A*, American Physical Society, 2018, 97 (6), pp.063614 (1-14). 〈10.1103/PhysRevA.97.063614〉We study analytically the Wigner function W N (x,p) of N noninteracting fermions trapped in a smooth confining potential V (x) in d dimensions. At zero temperature, W N (x,p) is constant over a finite support in the phase space (x,p) and vanishes outside. Near the edge of this support, we find a universal scaling behavior of W N (x,p) for large N. The associated scaling function is independent of the precise shape of the potential as well as the spatial dimension d. We further generalize our results to finite temperature T > 0. We show that there exists a low-temperature regime T ∼ e N /b, where e N is an energy scale that depends on N and the confining potential V (x), where the Wigner function at the edge again takes a universal scaling form with a b-dependent scaling function. This temperature-dependent scaling function is also independent of the potential as well as the dimension d. Our results generalize to any d 1 and T 0 the d = 1 and T = 0 results obtained by Bettelheim and Wiegman [Phys. Rev. B 84, 085102 (2011)] (see also the earlier paper by Balazs and Zipfel [Ann. Phys. (NY) 77, 139 (1973)]).

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Universality Classes of Interaction Structures for NK Fitness Landscapes

### Sungmin Hwang

^{1, 2}Benjamin Schmiegelt^{2}Luca Ferretti^{3}Joachim Krug^{2}*Journal of Statistical Physics*, Springer Verlag, 2018, 172 (1), pp.226 - 278. 〈10.1007/s10955-018-1979-z〉Kauffman's NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of $L$ binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of $k \le L$ loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of $L$, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large $k$. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in $L$ for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Cologne
- 3. The Pirbright Institute

## Archive ouverte HAL – Towards Quantum Simulation with Circular Rydberg Atoms

### Thanh Long Nguyen

^{1}Jean-Michel Raimond^{1}Clément Sayrin^{1}Rodrigo Cortinas^{1}Tigrane Cantat-Moltrecht^{1}Fédéric Assemat^{1}Igor Dotsenko^{1}Sébastien Gleyzes^{1}Serge Haroche^{1}Guillaume Roux^{2}Thierry Jolicoeur^{2}Michel Brune^{1}*Physical Review X*, American Physical Society, 2018, 8 (1), 〈10.1103/PhysRevX.8.011032〉The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation.

- 1. LKB [Collège de France] - Laboratoire Kastler Brossel
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Topology of Disconnected Elementary Band Representations

### Jennifer Cano

^{1}Barry Bradlyn^{1}Zhijun Wang^{2}L. Elcoro^{3}M. g. Vergniory^{3}C. Felser^{4}M. i. Aroyo^{3}B. Andrei Bernevig^{5, 6, 7}*Physical Review Letters*, American Physical Society, 2018, 120 (26), 〈10.1103/PhysRevLett.120.266401〉Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a symmorphic and a non-symmorphic space group -- of elementary band representations realized with an energy gap. In doing so, we explicitly construct a counterexample to a claim by Michel and Zak that single-valued elementary band representations in non-symmorphic space groups with time-reversal symmetry are connected. For each example, we construct a topological invariant to explicitly demonstrate that the valence bands are non-trivial. We discover a new topological invariant: a movable but unremovable Dirac cone in the "Wilson Hamiltonian" and a bent-Z2 index.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. Princeton University
- 3. University of the Basque Country - University of the Basque Country
- 4. CPfS - Max Planck Institute for Chemical Physics of Solids
- 5. DPPU - Department of Physics,Princeton University
- 6. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 7. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Topological Zak Phase in Strongly-Coupled LC Circuits

### Tal Goren

^{1}Kirill Plekhanov^{1, 2}Félicien Appas^{1}Karyn Le Hur^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\cal Z}_2$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sub-lattice symmetry, represented by an anti-unitary transformation. We present a methos to measure the winding of the topological Zak phase across the Brillouin zone by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems. We study the robustness of edge modes towards disorder.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The open XXZ spin chain in the SoV framework: scalar product of separate states

### N. Kitanine

^{1}J.M. Maillet^{2}G. Niccoli^{2}V. Terras^{3}*J.Phys.A*, 2018, 51 (48), pp.485201. 〈10.1088/1751-8121/aae76f〉In our previous paper (Kitanine et al 2017 J. Phys. A: Math. Theor. 50 224001) we have obtained, for the XXX spin-1/2 Heisenberg open chain, new determinant representations for the scalar products of separate states in the quantum separation of variables (SoV) framework. In this article we perform a similar study in a more complicated case: the XXZ open spin-1/2 chain with the most general integrable boundary terms. We first revisit the SoV solution of this model using a matrix version of the Vertex-IRF gauge transformation so as to reduce one of the boundary K-matrices to a diagonal form. As usual within the SoV approach, the scalar products of separate states are computed in terms of dressed Vandermonde determinants having an intricate dependency on the inhomogeneity parameters. We show that these determinants can be transformed into different ones in which the homogeneous limit can be taken straightforwardly. These representations generalize in a non-trivial manner to the trigonometric case the expressions found previously in the rational case. We also show that generically all scalar products can be expressed in a form which is similar to—although more cumbersome than—the well-known Slavnov determinant representation for the scalar products of the Bethe states of the periodic chain. Considering a special choice of the boundary parameters relevant in the thermodynamic limit to describe the half infinite chain with a general boundary, we particularize these representations to the case of one of the two states being an eigenstate. We obtain simplified formulas that should be of direct use to compute the form factors and correlation functions of this model.

- 1. IMB - Institut de Mathématiques de Bourgogne [Dijon]
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The impact of the injection protocol on an impurity’s stationary state

### Oleksandr Gamayun

^{1, 2}Oleg Lychkovskiy^{3, 4, 5}Evgeni Burovski^{6, 7}Matthew Malcomson^{8}Vadim V. Cheianov^{1}Mikhail B. Zvonarev^{9}*Physical Review Letters*, American Physical Society, 2018We examine stationary state properties of an impurity particle injected into a one-dimensional quantum gas. We show that the value of the impurity's end velocity lies between zero and the speed of sound in the gas, and is determined by the injection protocol. This way, the impurity's constant motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of Landau approach to superfluidity. We provide exact analytic results in the thermodynamic limit, and perform finite-size numerical simulations to demonstrate that the predicted phenomena are within the reach of the existing ultracold gases experiments.

- 1. Universiteit Leiden [Leiden]
- 2. Bogolyubov Institute for Theoretical Physics
- 3. Skoltech - Skolkovo Institute of Science and Technology [Moscow]
- 4. Steklov Mathematical Institute of Russian Academy of Sciences
- 5. Russian Quantum Center
- 6. National Research University Higher School of Economics [Moscow]
- 7. Science Center in Chernogolovka
- 8. Lancaster University
- 9. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The asymmetric Wigner bilayer

### Moritz Antlanger

^{1}Gerhard Kahl^{1}Martial Mazars^{2}Ladislav Samaj^{3}Emmanuel Trizac^{4}Ladislav Šamaj^{5}*Journal of Chemical Physics*, American Institute of Physics, 2018, 149 (24), pp.244904. 〈10.1063/1.5053651〉We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates, and form there ordered sublattices. Using complementary tools (analytic and numerical) we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied. The overwhelming plethora of emerging Wigner bilayer ground states can be understood in terms of the competition of two strategies of the system: the desire to guarantee net charge neutrality on each of the plates and the effort of the particles to self-organize into commensurate sublattices. The emerging structures range from simple, highly commensurate (and thus very stable) lattices (such as staggered structures, built up by simple motives) to structures with a complicated internal structure. The combined application of our two approaches (whose results agree within remarkable accuracy) allows to study on a quantitative level phenomena such as over- and underpopulation of the plates by the mobile particles, the nature of phase transitions between the emerging phases (which pertain to two different universality classes), and the physical laws that govern the long-range behaviour of the forces acting between the plates. Extensive Monte Carlo simulations, which have been carried out at small, but finite temperatures along selected, well-defined pathways in parameter space confirm the analytical and numerical predictions within high accuracy.

- 1. TU WIEN - Technical University of Vienna [Vienna]
- 2. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 3. Institute of Physics
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Institute of Physics, Slovak Academy of Sciences

## Archive ouverte HAL – Surface temperatures in New York City: Geospatial data enables the accurate prediction of radiative heat transfer

### Masoud Ghandehari

^{1}Thorsten Emig^{2, 3}Milad Aghamohamadnia^{1}*Scientific Reports*, Nature Publishing Group, 2018Three decades into the research seeking to derive the urban energy budget, the dynamics of the thermal exchange between the densely built infrastructure and the environment are still not well understood. We present a novel hybrid experimental-numerical approach for the analysis of the radiative heat transfer in New York City. The aim of this work is to contribute to the calculation of the urban energy budget, in particular the stored energy. Improved understanding of urban thermodynamics incorporating the interaction of the various bodies will have implications on energy conservation at the building scale, as well as human health and comfort at the urban scale. The platform presented is based on longwave hyperspectral imaging of nearly 100 blocks of Manhattan, and a geospatial radiosity model that describes the collective radiative heat exchange between multiple buildings. The close comparison of temperature values derived from measurements and the computed surface temperatures (including streets and roads) implies that this geospatial, thermodynamic numerical model applied to urban structures, is promising for accurate and high resolution analysis of urban surface temperatures.

- 1. NYU Tandon School of Engineering
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MSE2 - Multiscale Materials Science for Energy and Environment

## Archive ouverte HAL – Superfluidity of identical fermions in an optical lattice: Atoms and polar molecules

### A. K. Fedorov

^{1}V. I. Yudson^{2}G. V. Shlyapnikov^{3, 4, 1}*AIP Conference Proceedings*, American Institute of Physics, 2018, 〈10.1063/1.5025460〉In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.

- 1. Russian Quantum Center
- 2. Institute of Spectroscopy
- 3. Wuhan Institute of Physics and Mathematics
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases

### L. Samaj

^{1}M. Trulsson^{2}E. Trizac^{3}*Soft Matter*, Royal Society of Chemistry, 2018We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner Strong-Coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of $d$ comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.

- 1. Institute of Physics
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

### Kanaya Malakar

^{1}V. Jemseena^{2}Anupam Kundu^{2}K. Vijay Kumar^{2}Sanjib Sabhapandit^{3}Satya N. Majumdar^{4}S. Redner^{5}Abhishek Dhar^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2018We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.

- 1. Presidency University
- 2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 3. Raman Research Institute
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Santa Fe Institute

## Archive ouverte HAL – Statistical Properties of a Polymer Globule Formed during Collapse with the Irreversible Coalescence of Units

### A. M. AstakhovS. K. Nechaev

^{1}K. E. Polovnikov#### A. M. Astakhov, S. K. Nechaev, K. E. Polovnikov. Statistical Properties of a Polymer Globule Formed during Collapse with the Irreversible Coalescence of Units.

*Polymer Science*, Springer Link, 2018. ⟨hal-02365365⟩Collapse of the polymer chain upon the sharp decrease of solvent quality is studied. During collapse, any pair of polymer units appearing in a sufficiently close vicinity in space has the possibility with a certain probability to form an irreversible crosslink, thereby preventing the interpenetration of chain material between the forming clusters. Globular structures having different spatial chain packing at various scales are obtained by computer simulations. It is shown that the dependence of probability of contact between two monomers in space , where s is a distance between monomers along chain, reproduces a number of characteristic features observed previously in experiments on the analysis of three-dimensional chromatin packing. The cluster analysis of intramolecular contact maps makes it possible to express the hypothesis that there are characteristic discrete hierarchical levels in polymer packing associated with the number-theoretic origin of rare-event statistics and inherent to individual maps of intra- and interchromosomal contacts.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Stable $p$-wave resonant two-dimensional Fermi-Bose dimers

### Betzalel BazakDmitry S. Petrov

^{1}*Phys.Rev.Lett.*, 2018, 121, pp.263001. 〈10.1103/PhysRevLett.121.263001〉We consider two-dimensional weakly-bound heterospecies molecules formed in a Fermi-Bose mixture with attractive Fermi-Bose and repulsive Bose-Bose interactions. Bosonic exchanges lead to an intermolecular attraction, which can be controlled and tuned to a p-wave resonance. Such attractive fermionic molecules can be realized in quasi-two-dimensional ultracold isotopic or heteronuclear mixtures. We show that they are stable with respect to the recombination to deeply-bound molecular states and with respect to the formation of higher-order clusters (trimers, tetramers, etc.)

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Spectral content of fractional Brownian motion with stochastic reset

### Satya N Majumdar

^{1}Gleb Oshanin^{2}Satya Majumdar^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (43), 〈10.1088/1751-8121/aadef0〉We analyse the power spectral density (PSD) $S_T(f)$ (with $T$ being the observation time and $f$ is the frequency) of a fractional Brownian motion (fBm), with an arbitrary Hurst index $H \in (0,1)$, undergoing a stochastic resetting to the origin at a constant rate $r$ - the resetting process introduced some time ago as an example of an efficient, optimisable search algorithm. To this end, we first derive an exact expression for the covariance function of an arbitrary (not necessarily a fBm) process with a reset, expressing it through the covariance function of the parental process without a reset, which yields the desired result for the fBm in a particular case. We then use this result to compute exactly the power spectral density for fBM for all frequency $f$. The asymptotic, large frequency $f$ behaviour of the PSD turns out to be distinctly different for sub- $(H < 1/2)$ and super-diffusive $(H > 1/2)$ fBms. We show that for large $f$, the PSD has a power law tail: $S_T(f) \sim 1/f^{\gamma}$ where the exponent $\gamma= 2H+1$ for $0

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

## Archive ouverte HAL – Something interacting and solvable in 1D

### Eyzo StoutenPieter W. ClaeysMikhail Zvonarev

^{1}Jean-Sébastien CauxVladimir Gritsev*J.Phys.A*, 2018, 51 (48), pp.485204. 〈10.1088/1751-8121/aae8bb〉We present a two-parameter family of exactly solvable quantum many-body systems in one spatial dimension containing the Lieb–Liniger model of interacting bosons as a particular case. The principal building block of this construction is the previously-introduced (Stouten et al 2018 arXiv:1712.09375) family of two-particle scattering matrices. We discuss an transformation connecting the models within this family and make a correspondence with generalized point interactions. The Bethe equations for the ground state are discussed with a special emphasis on ‘non-interacting modes’ connected by the modular subgroup of . The bound state solutions are discussed and are conjectured to follow some correlated version of the string hypothesis. The excitation spectrum of the new models in this family is derived in analogy to the Lieb–Liniger model and we show that for certain choices of parameters a spectrum inversion occurs such that the Umklapp solutions become the new ground state.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?

### Xiangyu Cao

^{1, 2}Alexandre Nicolas^{1}Denny Trimcev^{1, 3}Alberto Rosso^{1}*Soft Matter*, Royal Society of Chemistry, 2018, 14 (18), pp.3640 - 3651. 〈10.1039/C7SM02510F〉The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like `impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of California [Berkeley]
- 3. ENS Paris - École normale supérieure - Paris

## Archive ouverte HAL – Singularities of Floquet scattering and tunneling

### H. Landa

^{1, 2}*Physical Review A*, American Physical Society, 2018, 97 (4), 〈10.1103/PhysRevA.97.042705〉We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive amplitude, making the S-matrix nonanalytic at a singular point. For the corresponding quasi-bound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low energy (s-wave) particles and their conversion to high energy outgoing (mostly p-) waves. We examine the relation of such Floquet singularities, lacking in an effective time independent approximation, with well known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power law forces and subject to periodic fields, e.g. co-trapped ions and atoms.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Archive ouverte HAL – Separating intrinsic interactions from extrinsic correlations in a network of sensory neurons

### Ulisse Ferrari

^{1}Stéphane Deny^{2}Matthew Chalk^{1}Gašper Tkačik^{3}Olivier Marre^{1}Thierry Mora^{4}*Physical Review E*, American Physical Society (APS), 2018, 98 (4), pp.042410. 〈10.1103/PhysRevE.98.042410〉Correlations in sensory neural networks have both extrinsic and intrinsic origins. Extrinsic or stimulus correlations arise from shared inputs to the network and, thus, depend strongly on the stimulus ensemble. Intrinsic or noise correlations reflect biophysical mechanisms of interactions between neurons, which are expected to be robust to changes in the stimulus ensemble. Despite the importance of this distinction for understanding how sensory networks encode information collectively, no method exists to reliably separate intrinsic interactions from extrinsic correlations in neural activity data, limiting our ability to build predictive models of the network response. In this paper we introduce a general strategy to infer population models of interacting neurons that collectively encode stimulus information. The key to disentangling intrinsic from extrinsic correlations is to infer the couplings between neurons separately from the encoding model and to combine the two using corrections calculated in a mean-field approximation. We demonstrate the effectiveness of this approach in retinal recordings. The same coupling network is inferred from responses to radically different stimulus ensembles, showing that these couplings indeed reflect stimulus-independent interactions between neurons. The inferred model predicts accurately the collective response of retinal ganglion cell populations as a function of the stimulus.

- 1. Institut de la Vision
- 2. Stanford University [Stanford]
- 3. IST - Institute of Science and Technology Austria [Klosterneuburg, Austria]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Run and tumble particle under resetting: a renewal approach

### Martin R. Evans

^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (47), pp.475003. 〈10.1088/1751-8121/aae74e〉We consider a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension. We study the addition of a Poissonian resetting process occurring with rate $r$. At a reset event the particle's position is returned to the resetting site $X_r$ and the particle's velocity is reversed with probability $\eta$. The case $\eta = 1/2$ corresponds to position resetting and velocity randomization whereas $\eta =0$ corresponds to position-only resetting. We show that, beginning from symmetric initial conditions, the stationary state does not depend on $\eta$ i.e. it is independent of the velocity resetting protocol. However, in the presence of an absorbing boundary at the origin, the survival probability and mean time to absorption do depend on the velocity resetting protocol. Using a renewal equation approach, we show that the the mean time to absorption is always less for velocity randomization than for position-only resetting.

- 1. SUPA, School of Physics, University of Edinburgh
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Role of City Texture in Urban Heat Islands at Nighttime

### J.M. SobstylT. Emig

^{1}M.J. Abdolhosseini QomiF.-J. UlmRoland J.-M. Pellenq^{2, 3}*Phys.Rev.Lett.*, 2018, 120 (10), pp.108701. 〈10.1103/PhysRevLett.120.108701〉An urban heat island (UHI) is a climate phenomenon that results in an increased air temperature in cities when compared to their rural surroundings. In this Letter, the dependence of an UHI on urban geometry is studied. Multiyear urban-rural temperature differences and building footprints data combined with a heat radiation scaling model are used to demonstrate for more than 50 cities worldwide that city texture—measured by a building distribution function and the sky view factor—explains city-to-city variations in nocturnal UHIs. Our results show a strong correlation between nocturnal UHIs and the city texture.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. MIT - Massachusetts Institute of Technology
- 3. CINaM - Centre Interdisciplinaire de Nanoscience de Marseille

## Archive ouverte HAL – Role of Cis, Trans, and Inbreeding Effects on Meiotic Recombination in Saccharomyces cerevisiae

### Xavier Raffoux

^{1}Mickael Bourge^{2, 3, 4, 5}Fabrice Dumas^{1}Olivier C. Martin^{6, 1}Matthieu Falque^{1}#### Xavier Raffoux, Mickael Bourge, Fabrice Dumas, Olivier C. Martin, Matthieu Falque. Role of Cis, Trans, and Inbreeding Effects on Meiotic Recombination in Saccharomyces cerevisiae.

*GENETICS*, 2018, 210 (4), pp.1213--1226. ⟨10.1534/genetics.118.301644⟩. ⟨hal-02183493⟩Meiotic recombination is a major driver of genome evolution by creating new genetic combinations. To probe the factors driving variability of meiotic recombination, we used a high-throughput method to measure recombination rates in hybrids between SK1 and a total of 26 Saccharomyces cerevisiae strains from different geographic origins and habitats. Fourteen intervals were monitored for each strain, covering chromosomes VI and XI entirely, and part of chromosome I. We found an average number of crossovers per chromosome ranging between 1.0 and 9.5 across strains ("domesticated" or not), which is higher than the average between 0.5 and 1.5 found in most organisms. In the different intervals analyzed, recombination showed up to ninefold variation across strains but global recombination landscapes along chromosomes varied less. We also built an incomplete diallel experiment to measure recombination rates in one region of chromosome XI in 10 different crosses involving five parental strains. Our overall results indicate that recombination rate is increasingly positively correlated with sequence similarity between homologs (i) in DNA double-strand-break-rich regions within intervals, (ii) in entire intervals, and (iii) at the whole genome scale. Therefore, these correlations cannot be explained by cis effects only. We also estimated that cis and trans effects explained 38 and 17%, respectively, of the variance of recombination rate. In addition, by using a quantitative genetics analysis, we identified an inbreeding effect that reduces recombination rate in homozygous genotypes, while other interaction effects (specific combining ability) or additive effects (general combining ability) are found to be weak. Finally, we measured significant crossover interference in some strains, and interference intensity was positively correlated with crossover number.

- 1. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)
- 2. I2BC - Institut de Biologie Intégrative de la Cellule
- 3. Plateforme intégrée IMAGIF
- 4. PF I2BC - Département Plateforme
- 5. CYTO - Cytométrie
- 6. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience

### Silvia Grigolon

^{1}Barbara Bravi^{2}Olivier C. Martin^{1, 3}#### Silvia Grigolon, Barbara Bravi, Olivier C. Martin. Responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience.

*Royal Society Open Science*, The Royal Society, 2018, 5 (1), pp.1-15. ⟨10.1098/rsos.172098⟩. ⟨hal-01735356⟩Plants depend on the signaling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signaling network involves a negative feedback at the level of the Aux/IAA proteins which mediate the influence of auxin (the signal) on the ARF transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signaling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative regulatory feedback loop allows the system to have a far larger sensitivity in its dynamical response to auxin. At the same time, this sensitivity does not prevent the system from being highly resilient. Given this insight, we reconsider previously published models and build a new quantitative and calibrated biomolecular model of auxin signaling.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. King‘s College London
- 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)

## Archive ouverte HAL – Reaction kinetics of ultracold molecule-molecule collisions

### Daniel K. Hoffmann

^{1}Thomas Paintner^{1}Wolfgang Limmer^{1}Dmitry S. Petrov^{2}Johannes Hecker Denschlag^{1}*Nature Communications*, Nature Publishing Group, 2018Studying chemical reactions on a state-to-state level tests and improves our fundamental understanding of chemical processes. For such investigations it is convenient to make use of ultracold atomic and molecular reactants as they can be prepared in well defined internal and external quantum states$^{1-4}$. In general, even cold reactions have many possible final product states$^{5-15}$ and reaction channels are therefore hard to track individually$^{16}$. In special cases, however, only a single reaction channel is essentially participating, as observed e.g. in the recombination of two atoms forming a Feshbach molecule$^{17-19}$ or in atom-Feshbach molecule exchange reactions$^{20,21}$. Here, we investigate a single-channel reaction of two Li$_2$-Feshbach molecules where one of the molecules dissociates into two atoms $2\mathrm{AB}\Rightarrow \mathrm{AB}+\mathrm{A}+\mathrm{B}$. The process is a prototype for a class of four-body collisions where two reactants produce three product particles. We measure the collisional dissociation rate constant of this process as a function of collision energy/ temperature and scattering length. We confirm an Arrhenius-law dependence on the collision energy, an $a^4$ power-law dependence on the scattering length $a$ and determine a universal four body reaction constant.

- 1. Ulm University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Quantum purification spectroscopy

### Bradraj Pandey

^{1}Kirill Plekhanov^{1, 2}Guillaume Roux^{1}*Phys.Rev.A*, 2018, 98 (5), pp.050103. 〈10.1103/PhysRevA.98.050103〉We discuss a protocol based on quenching a purified quantum system that allows one to capture bulk spectral features. It uses an infinite temperature initial state and an interferometric strategy to access the Loschmidt amplitude, from which the spectral features are retrieved via Fourier transform, providing coarse-grained approximation at finite times. It involves techniques available in current experimental setups for quantum simulation, at least for small systems. We illustrate possible applications in testing the eigenstate thermalization hypothesis and the physics of many-body localization.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CPHT - Centre de Physique Théorique [Palaiseau]

## Archive ouverte HAL – Quantum dynamics with stochastic reset

### B. Mukherjee

^{1}K. Sengupta^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 98 (10), 〈10.1103/PhysRevB.98.104309〉We study non-equilibrium dynamics of integrable and non-integrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate $r$, that project the system to its initial state. We show that the steady state density matrix of a non-integrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite $r$. Consequently a generic observable $\hat O$, whose expectation value receives contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite $r$. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles (GGE s) characterized by $r$. We also study the spread of particle density of a non-interacting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.

- 1. Indian Association for the Cultivation of Sciences
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Power-law random banded matrices and ultrametric matrices: Eigenvector distribution in the intermediate regime

### Eugene Bogomolny

^{1}Martin Sieber^{2}*Physical Review E*, American Physical Society (APS), 2018- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Bristol [Bristol]

## Archive ouverte HAL – Post-Ehrenfest many-body quantum interferences in ultracold atoms far out of equilibrium

### Steven Tomsovic

^{1, 2}Peter Schlagheck^{3}Denis Ullmo^{4}Juan Diego Urbina^{1}Klaus Richter^{1}Juan-Diego Urbina*Physical Review A*, American Physical Society, 2018, 97 (6), 〈10.1103/PhysRevA.97.061606〉Far out-of-equilibrium many-body quantum dynamics in isolated systems necessarily generate interferences beyond an Ehrenfest time scale, where quantum and classical expectation values diverge. Of great recent interest is the role these interferences play in the spreading of quantum information across the many degrees of freedom, i.e.~scrambling. Ultracold atomic gases provide a promising setting to explore these phenomena. Theoretically speaking, the heavily-relied-upon truncated Wigner approximation leaves out these interferences. We develop a semiclassical theory which bridges classical and quantum concepts in many-body bosonic systems and properly incorporates such missing quantum effects. For mesoscopically populated Bose-Hubbard systems, it is shown that this theory captures post-Ehrenfest quantum interference phenomena very accurately, and contains relevant phase information to perform many-body spectroscopy with high precision.

- 1. UR - Universität Regensburg
- 2. WSU - Washington State University
- 3. ULg - Institut de Physique
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Planar screening by charge polydisperse counterions

### M. Trulsson

^{1, 2}E. Trizac^{1}L. Samaj^{3}*Journal of Physics: Condensed Matter*, IOP Publishing, 2018, 30 (3), 〈10.1088/1361-648X/aa9a79〉We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane plate, when the counterions are characterised by a distribution of charges (or valence), $n(q)$. We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions $n(q)$, for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous $n(q)$ behaviour is already featured by discrete mixtures with a relatively small number of constituents.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Lund University [Lund]
- 3. Institute of Physics

## Archive ouverte HAL – Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

### Xiangyu Cao

^{1}Vincent Démery^{2, 3}Alberto Rosso^{4, 5}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (23), 〈10.1088/1751-8121/aac02f〉The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility ${\mu}_{\text{eff}}$ . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force $f_c$. At small disorder, we unveil an intermediary linear regime for $f_c < f < 1$ characterized by the renormalized mobility ${\mu}_{\text{eff}}$. Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

- 1. University of California [Berkeley]
- 2. ESPCI - UMR Gulliver
- 3. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. KITP - Kavli Institute for Theoretical Physics

## Archive ouverte HAL – Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions

### V. Roberdel

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1, 3}*Physical Review A*, American Physical Society, 2018, 97 (5), 〈10.1103/PhysRevA.97.053419〉We present a comprehensive phase-space treatment of the motion of charged particles in electrodynamic traps. Focusing on five-wire surface-electrode Paul traps, we study the details of integrable and chaotic motion of a single ion. We introduce appropriate phase-space measures and give a universal characterization of the trap effectiveness as a function of the parameters. We rigorously derive the commonly used (time-independent) pseudopotential approximation, quantify its regime of validity and analyze the mechanism of its breakdown within the time-dependent potential. The phase space approach that we develop gives a general framework for describing ion dynamics in a broad variety of surface Paul traps. To probe this framework experimentally, we propose and analyze, using numerical simulations, an experiment that can be realized with an existing four-wire trap. We predict a robust experimental signature of the existence of trapping pockets within a mixed regular and chaotic phase-space structure. Intricately rich escape dynamics suggest that surface traps give access to exploring microscopic Hamiltonian transport phenomena in phase space.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technologies
- 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Archive ouverte HAL – Origins and diagnostics of the nonequilibrium character of active systems

### Lokrshi Prawar Dadhichi

^{1}Ananyo Maitra^{2}Sriram Ramaswamy^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018We present in detail a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath. We apply the formalism to clarify issues of principle regarding the sources and signatures of nonequilibrium behaviour in a variety of polar and apolar single-particle systems and polar flocks. We show that distance from thermal equilibrium depends on how time-reversal is implemented and hence on the reference equilibrium state. We predict characteristic forms for the frequency-resolved entropy production for an active polar particle in a harmonic potential, which should be testable in experiments.

- 1. TIFR - Tata Institute of Fundamental Research [Hyderabad]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IISc Bangalore - Indian Institute of Science [Bangalore]

## Archive ouverte HAL – Orientation of plastic rearrangements in two-dimensional model glasses under shear

### Alexandre Nicolas

^{1}Jörg Rottler^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2018, 97, pp.063002. 〈https://journals.aps.org/pre/pdf/10.1103/PhysRevE.97.063002〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. UBC - University of British Columbia

## Archive ouverte HAL – Optimal localization patterns in bacterial protein synthesis

### Jacky NguyenMichele Castellana

^{1}#### Jacky Nguyen, Michele Castellana. Optimal localization patterns in bacterial protein synthesis.

*Physical Review E*, American Physical Society (APS), 2018, 98 (3), ⟨10.1103/PhysRevE.98.032417⟩. ⟨hal-02390875⟩In $\textit{Escherichia coli}$ bacterium, the molecular compounds involved in protein synthesis, messenger RNAs (mRNAs) and ribosomes, show marked intracellular localization patterns. Yet a quantitative understanding of the physical principles which would allow one to control protein synthesis by designing, bioengineering, and optimizing these localization patterns is still lacking. In this study, we consider a scenario where a synthetic modification of mRNA reaction-diffusion properties allows for controlling the localization and stoichiometry of mRNAs and polysomes$\mathrm{-}$complexes of multiple ribosomes bound to mRNAs. Our analysis demonstrates that protein synthesis can be controlled, e.g., optimally enhanced or inhibited, by leveraging mRNA spatial localization and stoichiometry only, without resorting to alterations of mRNA expression levels. We identify the physical mechanisms that control the protein-synthesis rate, highlighting the importance of colocalization between mRNAs and freely diffusing ribosomes, and the interplay between polysome stoichiometry and excluded-volume effects due to the DNA nucleoid. The genome-wide, quantitative predictions of our work may allow for a direct verification and implementation in cell-biology experiments, where localization patterns and protein-synthesis rates may be monitored by fluorescence microscopy in single cells and populations.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models

### Xiangyu CaoPierre Le Doussal

^{1}Alberto Rosso^{2}Raoul Santachiara^{2}*Phys.Rev.E*, 2018, 97 (4), pp.042111. 〈10.1103/PhysRevE.97.042111〉We study transitions in log-correlated random energy models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a., pre-freezing). By means of LFT-logREM mapping, replica symmetry breaking and traveling-wave equation techniques, we unify both transitions in a two-parameter diagram, which describes the free-energy large deviations of logREMs with a deterministic background log potential, or equivalently, the joint moments of the free energy and Gibbs measure in logREMs without background potential. Under the LFT-logREM mapping, the transitions correspond to the competition of discrete and continuous terms in a four-point correlation function. Our results provide a statistical interpretation of a peculiar nonlocality of the operator product expansion in LFT. The results are rederived by a traveling-wave equation calculation, which shows that the features of LFT responsible for the transitions are reproduced in a simple model of diffusion with absorption. We examine also the problem by a replica symmetry breaking analysis. It complements the previous methods and reveals a rich large deviation structure of the free energy of logREMs with a deterministic background log potential. Many results are verified in the integrable circular logREM, by a replica-Coulomb gas integral approach. The related problem of common length (overlap) distribution is also considered. We provide a traveling-wave equation derivation of the LFT predictions announced in a precedent work.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – One-dimensional three-boson problem with two- and three-body interactions

### G. Guijarro

^{1}A. Pricoupenko^{2, 3}G. E. Astrakharchik^{1}J. Boronat^{1}D. S. Petrov^{2}*Physical Review A*, American Physical Society, 2018, 97 (6), 〈10.1103/PhysRevA.97.061605〉We solve the three-boson problem with contact two- and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies. Then, by using the diffusion Monte Carlo technique we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions. Combining these results with our three-body analytics we extract the three-dimer scattering length close to the dimer-dimer zero crossing. In both considered cases the three-dimer interaction turns out to be repulsive. Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion.

- 1. UPC - Universitat Politècnica de Catalunya [Barcelona]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. ENS Lyon - École normale supérieure - Lyon

## Archive ouverte HAL – On characteristic polynomials for a generalized chiral random matrix ensemble with a source

### Yan FyodorovJacek Grela

^{1}Eugene Strahov*J.Phys.A*, 2018, 51 (13), pp.134003. 〈10.1088/1751-8121/aaae2a〉We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models

### Nina Javerzat

^{1}Raoul Santachiara^{1}Omar Foda*JHEP*, 2018, 08, pp.183. 〈10.1007/JHEP08(2018)183〉We study Virasoro minimal-model 4-point conformal blocks on the sphere and 0-point conformal blocks on the torus (the Virasoro characters), as solutions of Zamolodchikov-type recursion relations. In particular, we study the singularities due to resonances of the dimensions of conformal fields in minimal-model representations, that appear in the intermediate steps of solving the recursion relations, but cancel in the final results.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Nontopological parafermions in a one-dimensional fermionic model with even multiplet pairing

### Leonardo Mazza

^{1, 2}Fernando IeminiMarcello DalmonteChristophe Mora^{3}*Phys.Rev.B*, 2018, 98 (20), pp.201109. 〈10.1103/PhysRevB.98.201109〉We discuss a one-dimensional fermionic model with a generalized ZN even multiplet pairing extending Kitaev Z2 chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a ZN symmetry enforcing an N-fold degenerate ground state robust to certain disorders. Interestingly, we show that the system supports a pair of parafermions but they are nonlocal instead of being boundary operators. As a result, the degeneracy of the ground state is only partly topological and coexists with spontaneous symmetry breaking by a (two-particle) pairing field. Each symmetry-breaking sector is shown to possess a pair of Majorana edge modes encoding the topological twofold degeneracy. Surrounded by two band insulators, the model exhibits for N=4 the dual of an 8π fractional Josephson effect highlighting the presence of parafermions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris
- 3. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

### Christophe Texier

^{1, 2}Johannes Mitscherling^{1, 3}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 〈10.02214〉We study the non-linear conductance $\mathcal{G}\sim\partial^2I/\partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim0.006\,E_\mathrm{Th}^{-1}$ (and $\langle\mathcal{G}\rangle=0$), where $E_\mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $\mathcal{G}_a\sim0.001\,(gE_\mathrm{Th})^{-1}$, where $g\gg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_\varphi\ll L$, where $L_\varphi$ is the phase coherence length, we get $\mathcal{G}\sim(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$, and $\mathcal{G}_a\sim(L_\varphi/L)^{11/2}(gE_\mathrm{Th})^{-1}\ll\mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_\varphi\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim(L_T/L)(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $\mathcal{G}_a\sim(L_T/L)^2(L_\varphi/L)^{7/2}(gE_\mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides
- 3. Max Planck Institute for Solid State Research

## Archive ouverte HAL – Non-interacting fermions in hard-edge potentials

### Bertrand Lacroix-A-Chez-Toine

^{1}Pierre Le Doussal^{2}Satya Majumdar^{1}Gregory Schehr^{1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018, 2018 (12), pp.123103. 〈10.1088/1742-5468/aaeda0〉We consider the spatial quantum and thermal fluctuations of non-interacting Fermi gases of $N$ particles confined in $d$-dimensional non-smooth potentials. We first present a thorough study of the spherically symmetric pure hard-box potential, with vanishing potential inside the box, both at $T=0$ and $T>0$. We find that the correlations near the wall are described by a "hard edge" kernel, which depend both on $d$ and $T$, and which is different from the "soft edge" Airy kernel, and its higher $d$ generalizations, found for smooth potentials. We extend these results to the case where the potential is non-uniform inside the box, and find that there exists a family of kernels which interpolate between the above "hard edge" kernel and the "soft edge" kernels. Finally, we consider one-dimensional singular potentials of the form $V(x)\sim |x|^{-\gamma}$ with $\gamma>0$. We show that the correlations close to the singularity at $x=0$ are described by this "hard edge" kernel for $1\leq\gamma<2$ while they are described by a broader family of "hard edge" kernels known as the Bessel kernel for $\gamma=2$ and, finally by the Airy kernel for $\gamma>2$. These one-dimensional kernels also appear in random matrix theory, and we provide here the mapping between the $1d$ fermion models and the corresponding random matrix ensembles. Part of these results were announced in a recent Letter, EPL 120, 10006 (2017).

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Negative Differential Mobility in Interacting Particle Systems

### Amit Kumar Chatterjee

^{1}Urna Basu^{2}P. K. Mohanty^{1}*Physical Review E*, American Physical Society (APS), 2018Driven particles in presence of crowded environment, obstacles or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. We propose a new mechanism for complex many-particle systems where slowing down of certain {\it non-driven} degrees of freedom by the external field can give rise to NDM. This phenomenon, resulting from inter-particle interactions, is illustrated in a pedagogical example of two interacting random walkers, one of which is biased by an external field while the same field only slows down the other keeping it unbiased. We also introduce and solve exactly the steady state of several driven diffusive systems, including a two species exclusion model, asymmetric misanthrope and zero-range processes, to show explicitly that this mechanism indeed leads to NDM.

- 1. Saha Institute of Nuclear Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Multicritical Edge Statistics for the Momenta of Fermions in Nonharmonic Traps

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}Pierre Le Doussal^{1}Satya Majumdar^{2}*Physical Review Letters*, American Physical Society, 2018, 121 (3), 〈10.1103/PhysRevLett.121.030603〉We compute the joint statistics of the momenta $p_i$ of $N$ non-interacting fermions in a trap, near the Fermi edge, with a particular focus on the largest one $p_{\max}$. For a $1d$ harmonic trap, momenta and positions play a symmetric role and hence, the joint statistics of momenta is identical to that of the positions. In particular, $p_{\max}$, as $x_{\max}$, is distributed according to the Tracy-Widom distribution. Here we show that novel "momentum edge statistics" emerge when the curvature of the potential vanishes, i.e. for "flat traps" near their minimum, with $V(x) \sim x^{2n}$ and $n>1$. These are based on generalisations of the Airy kernel that we obtain explicitly. The fluctuations of $p_{\max}$ are governed by new universal distributions determined from the $n$-th member of the second Painlev\'e hierarchy of non-linear differential equations, with connections to multicritical random matrix models. Finite temperature extensions and possible experimental signatures in cold atoms are discussed.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Momentum distribution and coherence of a weakly interacting Bose gas after a quench

### Giovanni I. Martone

^{1}Pierre-Elie Larré^{2}Alessandro Fabbri^{3}Nicolas Pavloff^{1}*Phys.Rev.A*, 2018, 98 (6), pp.063617. 〈10.1103/PhysRevA.98.063617〉We consider a weakly interacting uniform atomic Bose gas with a time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov treatment we investigate the time evolution of several observables, including the momentum distribution, the degree of coherence in the system, and their dependence on dimensionality and temperature. We rigorously prove that the low-momentum Bogoliubov modes remain frozen during the whole evolution, while the high-momentum ones adiabatically follow the change in time of the interaction strength. At intermediate momenta we point out the occurrence of oscillations, which are analogous to Sakharov oscillations. We identify two wide classes of time-dependent behaviors of the coupling for which an exact solution of the problem can be found, allowing for an analytic computation of all the relevant observables. A special emphasis is put on the study of the coherence property of the system in one spatial dimension. We show that the system exhibits a smooth “light-cone effect,” with typically no prethermalization.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTM - Laboratoire de Physique Théorique et Modélisation
- 3. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

## Archive ouverte HAL – Momentum correlations as signature of sonic Hawking radiation in Bose-Einstein condensates

### A. Fabbri

^{1}N. Pavloff^{2}*SciPost Phys.*, 2018, 4, pp.019. 〈10.21468/SciPostPhys.4.4.019〉We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quenches.

- 1. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Modified Szegö–Widom Asymptotics for Block Toeplitz Matrices with Zero Modes

### E. BasorJerome Dubail

^{1}T. Emig^{2}R. Santachiara^{3}*Journal of Statistical Physics*, Springer Verlag, 2018- 1. LPCT - Laboratoire de Physique et Chimie Théoriques
- 2. MIT - Massachusetts Institute of Technology
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Modeling of networks and globules of charged domain walls observed in pump and pulse induced states

### Petr Karpov

^{1}Serguei Brazovskii^{2, 1, 3}*Scientific Reports*, Nature Publishing Group, 2018Experiments on optical and STM injection of carriers in layered $\mathrm{MX_2}$ materials revealed the formation of nanoscale patterns with networks and globules of domain walls. This is thought to be responsible for the metallization transition of the Mott insulator and for stabilization of a "hidden" state. In response, here we present studies of the classical charged lattice gas model emulating the superlattice of polarons ubiquitous to the material of choice $1T-\mathrm{TaS_2}$. The injection pulse was simulated by introducing a small random concentration of voids which subsequent evolution was followed by means of Monte Carlo cooling. Below the detected phase transition, the voids gradually coalesce into domain walls forming locally connected globules and then the global network leading to a mosaic fragmentation into domains with different degenerate ground states. The obtained patterns closely resemble the experimental STM visualizations. The surprising aggregation of charged voids is understood by fractionalization of their charges across the walls' lines.

- 1. MISIS - National University of Science and Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IJS - Jozef Stefan Institute [Ljubljana, Slovenia]

## Archive ouverte HAL – Matrix product state description of Halperin states

### V. Crépel

^{1}B. Estienne^{2}B.A. Bernevig^{1, 3}P. Lecheminant^{4}N. Regnault^{1}*Phys.Rev.B*, 2018, 97 (16), pp.165136. 〈10.1103/PhysRevB.97.165136〉Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.

- 1. LPA - Laboratoire Pierre Aigrain
- 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. LPTM - Laboratoire de Physique Théorique et Modélisation

## Archive ouverte HAL – Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

### Thomas Barthel

^{1, 2}Caterina De Bacco^{2, 3}Silvio Franz^{2}*Physical Review E*, American Physical Society (APS), 2018, 97 (1), 〈10.1103/PhysRevE.97.010104〉We introduce and apply a novel efficient method for the precise simulation of stochastic dynamical processes on locally tree-like graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, the new approach is based on a matrix product approximation of the so-called edge messages -- conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both, single instances as well as the thermodynamic limit. We employ it to examine prototypical non-equilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

- 1. Duke university [Durham]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Santa Fe Institute

## Archive ouverte HAL – Mapping the Calogero model on the Anyon model

### Stéphane Ouvry

^{1}Alexios P. Polychronakos*Nucl.Phys.B*, 2018, 936, pp.189-205. 〈10.1016/j.nuclphysb.2018.09.011〉We explicitly map the N -body one dimensional Calogero eigenstates in a harmonic well to the lowest Landau level sector of N -body eigenstates of the two dimensional anyon model in a harmonic well. The mapping is achieved in terms of a convolution kernel that uses as input the scattering eigenstates of the free Calogero model on the infinite line, which are obtained in an operator formulation.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Log-correlated random-energy models with extensive free-energy fluctuations: Pathologies caused by rare events as signatures of phase transitions

### Xiangyu Cao

^{1}Yan FyodorovPierre Le Doussal^{2}*Phys.Rev.E*, 2018, 97 (2), pp.022117. 〈10.1103/PhysRevE.97.022117〉We address systematically an apparent nonphysical behavior of the free-energy moment generating function for several instances of the logarithmically correlated models: the fractional Brownian motion with Hurst index H=0 (fBm0) (and its bridge version), a one-dimensional model appearing in decaying Burgers turbulence with log-correlated initial conditions and, finally, the two-dimensional log-correlated random-energy model (logREM) introduced in Cao et al. [Phys. Rev. Lett. 118, 090601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.090601] based on the two-dimensional Gaussian free field with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly nonphysical vanishing of the moment generating function for some values of parameters is related to the termination point transition (i.e., prefreezing). We study the associated universal log corrections in the frozen phase, both for logREMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the nontrivial free-energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Localization of soft modes at the depinning transition

### Xiangyu Cao

^{1}Sebastián Bouzat^{2}Alejandro B. Kolton^{2}Alberto Rosso^{1}*Physical Review E*, American Physical Society (APS), 2018, 97 (2), 〈10.1103/PhysRevE.97.022118〉We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead very similar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter of avalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection between its localization length and the Larkin length of the depinning model. In the fully connected model, the weak--strong pinning transition coincides with a peculiar localization transition of the ground state.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centro Atómico Bariloche [Argentine]

## Archive ouverte HAL – Liquid beyond the van der Waals paradigm

### Dmitry Petrov

^{1}*Nature Physics*, Nature Publishing Group, 2018, 14 (3), pp.211 - 212. 〈10.1038/s41567-018-0052-9〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Like-charge attraction in a one-dimensional setting: the importance of being odd

### E. Trizac

^{1}G. Tellez^{2}*European Journal of Physics*, European Physical Society, 2018From cement cohesion to DNA condensation, a proper statistical physics treatment of systems with long range forces is important for a number of applications in physics, chemistry, and biology. We compute here the effective force between fixed charged macromolecules, screened by oppositely charged mobile ions (counterions). We treat the problem in a one dimensional configuration, that allows for interesting discussion and derivation of exact results, remaining at a level of mathematical difficulty compatible with an undergraduate course. Emphasis is put on the counter-intuitive but fundamental phenomenon of like-charge attraction, that our treatment brings for the first time to the level of undergraduate teaching. The parity of the number of counterions is shown to play a prominent role, which sheds light on the binding mechanism at work when like-charge macromolecules do attract.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departamento de Fisica

## Archive ouverte HAL – Large deviations of convex hulls of self-avoiding random walks

### Hendrik Schawe

^{1}Alexander K. Hartmann^{2}Satya N. Majumdar^{3}Alexander HartmannSatya Majumdar^{3}*Physical Review E*, American Physical Society (APS), 2018, 97 (6), 〈10.1103/PhysRevE.97.062159〉A global picture of a random particle movement is given by the convex hull of the visited points. We obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of self-avoiding random walks, namely the classical Self-Avoiding Walk, the Smart-Kinetic Self-Avoiding Walk, and the Loop-Erased Random Walk. To obtain a comprehensive description of the measured random quantities, we applied sophisticated large-deviation techniques, which allowed us to obtain the distributions over a large range of the support down to probabilities far smaller than $P = 10^{-100}$ . We give an approximate closed form of the so-called large-deviation rate function $\Phi$ which generalizes above the upper critical dimension to the previously studied case of the standard random walk. Further we show correlations between the two observables also in the limits of atypical large or small values.

- 1. University of Oldenburg
- 2. Institut für Physik
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Jak-TGFβ cross-talk links transient adipose tissue inflammation to beige adipogenesis

### Rohollah BabaeiMaximilian SchusterIrina MelnSarah LerchRayane Ghandour

^{1}Didier Pisani^{2}Irem Bayindir-BuchhalterJulia MarxShuang Wu^{3}Gabriele SchoiswohlAdrian BilleterDamir KrunicJan MauerYun-Hee LeeJames GrannemanLars FischerBeat Müller-StichEz-Zoubir Amri^{4}Erin KershawMathias Heikenwalder^{5}Stephan Herzig^{6}Alexandros Vegiopoulos#### Rohollah Babaei, Maximilian Schuster, Irina Meln, Sarah Lerch, Rayane Ghandour, et al.. Jak-TGFβ cross-talk links transient adipose tissue inflammation to beige adipogenesis.

*Science Signaling*, American Association for the Advancement of Science, 2018, 11 (527), pp.eaai7838. ⟨10.1126/scisignal.aai7838⟩. ⟨hal-02398432⟩- 1. IBV - Institut de Biologie Valrose
- 2. LP2M - Laboratoire de PhysioMédecine Moléculaire
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. IBV - Institut de Biologie Valrose
- 5. Technische Universitat Munchen
- 6. Department Molecular Metabolic Control

## Archive ouverte HAL – Integrated Strategy for Lead Optimization Based on Fragment Growing: The Diversity-Oriented-Target-Focused-Synthesis Approach

### Laurent Hoffer

^{1}Yuliia VoitovichBrigitt Raux^{2}Kendall CarrascoChristophe Muller^{3}Aleksey Fedorov^{4}Carine Derviaux^{5}Agnès AmouricStéphane Betzi^{6}Dragos Horvath^{7}Alexandre Varnek^{8}Yves Collette^{6}Sébastien Combes^{9}Philippe Roche^{10}Xavier Morelli^{5}*Journal of Medicinal Chemistry*, American Chemical Society, 2018, 61 (13), pp.5719-5732. 〈10.1021/acs.jmedchem.8b00653〉- 1. Institut de Chimie de Strasbourg
- 2. EIPL - Enzymologie interfaciale et de physiologie de la lipolyse
- 3. IM2NP - Institut des Matériaux, de Microélectronique et des Nanosciences de Provence
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Institut Paoli-Calmettes
- 6. CRCM - Centre de Recherche en Cancérologie de Marseille
- 7. UGSF - Unité de Glycobiologie Structurale et Fonctionnelle - UMR 8576
- 8. Institut de Chimie de Strasbourg
- 9. ICR - Institut de Chimie Radicalaire
- 10. CRCM - Centre de Recherche en Cancérologie de Marseille

## Archive ouverte HAL – Hofstadter point spectrum trace and the Almost Mathieu operator

### Stephane Ouvry

^{1}Stephan Wagner^{2}Shuang Wu^{1}*Journal of Mathematical Physics*, American Institute of Physics (AIP), 2018We consider point spectrum traces in the Hofstadter model. We show how to recover the full quantum Hofstadter trace by integrating these point spectrum traces with the appropriate free density of states on the lattice. This construction is then generalized to the almost Mathieu operator and its n-th moments which can be expressed in terms of generalized Kreft coefficients.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Stellenbosch University

## Archive ouverte HAL – Higher-order corrections to the effective potential close to the jamming transition in the perceptron model

### Ada Altieri

^{1, 2}*Physical Review E*, American Physical Society (APS), 2018, 97 (1), 〈10.1103/PhysRevE.97.012103〉We analyze the perceptron model performing a Plefka-like expansion of the free energy. This model falls in the same universality class as hard spheres near jamming, allowing to get exact predictions in high dimensions for more complex systems. Our method enables to define an effective potential (or TAP free energy), namely a coarse-grained functional depending on the contact forces and the effective gaps between the particles. The derivation is performed up to the third order, with a particular emphasis on the role of third order corrections to the TAP free energy. These corrections, irrelevant in a mean-field framework in the thermodynamic limit, might instead play a fundamental role when considering finite-size effects. We also study the typical behavior of the forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. In our analysis, third order contributions vanish in the jamming limit, both for the potential and the generalized forces, in agreement with the argument proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the scalings emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.

- 1. Department of Physics [Roma La Sapienza]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – High-throughput measurement of recombination rates and genetic interference in Saccharomyces cerevisiae

### Xavier Raffoux

^{1}Mickael Bourge^{2, 3, 4, 5}Fabrice Dumas^{1}Olivier C. Martin^{6, 1}Matthieu Falque^{1}#### Xavier Raffoux, Mickael Bourge, Fabrice Dumas, Olivier C. Martin, Matthieu Falque. High-throughput measurement of recombination rates and genetic interference in Saccharomyces cerevisiae.

*Yeast (Chichester, England)*, 2018, 35 (6), pp.431--442. ⟨10.1002/yea.3315⟩. ⟨hal-02183495⟩Allelic recombination owing to meiotic crossovers is a major driver of genome evolution, as well as a key player for the selection of high-performing genotypes in economically important species. Therefore, we developed a high-throughput and low-cost method to measure recombination rates and crossover patterning (including interference) in large populations of the budding yeast Saccharomyces cerevisiae. Recombination and interference were analysed by flow cytometry, which allows time-consuming steps such as tetrad microdissection or spore growth to be avoided. Moreover, our method can also be used to compare recombination in wild-type vs. mutant individuals or in different environmental conditions, even if the changes in recombination rates are small. Furthermore, meiotic mutants often present recombination and/or pairing defects affecting spore viability but our method does not involve growth steps and thus avoids filtering out non-viable spores.

- 1. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)
- 2. I2BC - Institut de Biologie Intégrative de la Cellule
- 3. Plateforme intégrée IMAGIF
- 4. PF I2BC - Département Plateforme
- 5. CYTO - Cytométrie
- 6. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – High-precision simulation of the height distribution for the KPZ equation

### Alexander K. Hartmann

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Alberto Rosso^{3}Gregory Schehr^{3}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2018, 121 (6), 〈10.1209/0295-5075/121/67004〉The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10^{-1000} in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2 respectively, are preserved until large time. We present some evidence for the predicted non-trivial crossover in the left tail from the 5/2 tail exponent to the cubic tail of Tracy-Widom, although the details of the full scaling form remains beyond reach.

- 1. University of Oldenburg
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Ground-state energy of noninteracting fermions with a random energy spectrum

### Hendrik SchaweAlexander K. HartmannSatya N. Majumdar

^{1}Grégory Schehr^{1}*EPL*, 2018, 124 (4), pp.40005. 〈10.1209/0295-5075/124/40005〉We derive analytically the full distribution of the ground-state energy of K non-interacting fermions in a disordered environment, modelled by a Hamiltonian whose spectrum consists of N i.i.d. random energy levels with distribution (with ε ≥ 0), in the same spirit as the “Random Energy Model”. We show that for each fixed K, the distribution P K, N (E 0) of the ground-state energy E 0 has a universal scaling form in the limit of large N. We compute this universal scaling function and show that it depends only on K and the exponent α characterizing the small ε behaviour of . We compared the analytical predictions with results from numerical simulations. For this purpose we employed a sophisticated importance-sampling algorithm that allowed us to obtain the distributions over a large range of the support down to probabilities as small as . We found asymptotically a very good agreement between analytical predictions and numerical results.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Full Dysonian dynamics of the complex Ginibre ensemble

### Jacek Grela

^{1}Piotr Warchoł*J.Phys.A*, 2018, 51 (42), pp.425203. 〈10.1088/1751-8121/aadd54〉We find stochastic equations governing eigenvalues and eigenvectors of a dynamical complex Ginibre ensemble reaffirming the intertwined role played between both sets of matrix degrees of freedom. We solve the accompanying Smoluchowski–Fokker–Planck equation valid for any initial matrix. We derive evolution equations for the averaged extended characteristic polynomial and for a class of k-point eigenvalue correlation functions. From the latter we obtain a novel formula for the eigenvector correlation function which we inspect for Ginibre and spiric initial conditions and obtain macro- and microscopic limiting laws.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Fluctuations of observables for free fermions in a harmonic trap at finite temperature

### Aurélien Grabsch

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}Christophe Texier^{1}*SciPost Physics Journals*, the SciPost Foundation, 2018We study a system of 1D noninteracting spinless fermions in a confining trap at finite temperature. We first derive a useful and general relation for the fluctuations of the occupation numbers valid for arbitrary confining trap, as well as for both canonical and grand canonical ensembles. Using this relation, we obtain compact expressions, in the case of the harmonic trap, for the variance of certain observables of the form of sums of a function of the fermions' positions, $\mathcal{L}=\sum_n h(x_n)$. Such observables are also called linear statistics of the positions. As anticipated, we demonstrate explicitly that these fluctuations do depend on the ensemble in the thermodynamic limit, as opposed to averaged quantities, which are ensemble independent. We have applied our general formalism to compute the fluctuations of the number of fermions $\mathcal{N}_+$ on the positive axis at finite temperature. Our analytical results are compared to numerical simulations. We discuss the universality of the results with respect to the nature of the confinement.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Finite-Temperature Disordered Bosons in Two Dimensions

### G. Bertoli

^{1}V. p. Michal^{2}B. l. Altshuler^{3}G. v. Shlyapnikov^{1}*Physical Review Letters*, American Physical Society, 2018, 121 (3), 〈10.1103/PhysRevLett.121.030403〉We study phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. We identify superfluid, normal fluid, and insulator phases and construct the phase diagram. At T=0 one has a tricritical point where the three phases coexist. The truncation of the energy distribution at the trap barrier, which is a generic phenomenon in cold atom systems, limits the growth of the localization length and in contrast to the thermodynamic limit the insulator phase is present at any temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. TU Delft - Delft University of Technology
- 3. Columbia University [New York]

## Archive ouverte HAL – Extreme statistics and index distribution in the classical 1 d Coulomb gas

### Abhishek Dhar

^{1}Anupam Kundu^{1}Satya N. Majumdar^{2}Sanjib Sabhapandit^{3}Gregory Schehr^{2}Satya Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (29), 〈10.1088/1751-8121/aac75f〉We consider a one-dimensional gas of $N$ charged particles confined by an external harmonic potential and interacting via the one-dimensional Coulomb potential. For this system we show that in equilibrium the charges settle, on an average, uniformly and symmetrically on a finite region centred around the origin. We study the statistics of the position of the rightmost particle $x_{\max}$ and show that the limiting distribution describing its typical fluctuations is different from the Tracy-Widom distribution found in the one-dimensional log-gas. We also compute the large deviation functions which characterise the atypical fluctuations of $x_{\max}$ far away from its mean value. In addition, we study the gap between the two rightmost particles as well as the index $N_+$, i.e., the number of particles on the positive semi-axis. We compute the limiting distributions associated to the typical fluctuations of these observables as well as the corresponding large deviation functions. We provide numerical supports to our analytical predictions. Part of these results were announced in a recent Letter, Phys. Rev. Lett. 119, 060601 (2017).

- 1. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Raman Research Institute

## Archive ouverte HAL – Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

### Urna Basu

^{1, 2}Laurent Helden^{3}Matthias Krüger^{4, 3, 5}*Physical Review Letters*, American Physical Society, 2018, 120 (18), 〈10.1103/PhysRevLett.120.180604〉Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far from equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many body systems. It is illustrated in a four state model and in the near critical Ising model.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
- 3. University of Stuttgart
- 4. Max Planck Institute for Intelligent Systems
- 5. Georg-August-University [Göttingen]

## Archive ouverte HAL – Exponential number of equilibria and depinning threshold for a directed polymer in a random potential

### Yan V Fyodorov

^{1}Pierre Le Doussal^{2}Alberto Rosso^{3}Christophe Texier^{3}Yan Fyodorov^{4}Pierre Le Doussal^{2}*Annals of Physics*, 2018, 397, pp.1 - 64. 〈10.1016/j.aop.2018.07.029〉By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean number $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension $d=1+1$, grows exponentially $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle\sim\exp{(r\,L)}$ with its length $L$. The growth rate $r$ is found to be directly related to the generalised Lyapunov exponent (GLE) which is a moment-generating function characterising the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schr\"odinger operator of the 1D Anderson localization problem. For strong confinement, the rate $r$ is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate $r$ is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape "topology trivialization" phenomenon, we obtain an upper bound for the depinning threshold $f_c$, in the presence of an applied force, for elastic lines and $d$-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.

- 1. School of Mathematical Sciences [ Nottingham]
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. School of Mathematical Sciences [London]

## Archive ouverte HAL – Exactly solvable model for dynamic nuclear polarization

### Inés Rodríguez-Arias

^{1}Markus Müller^{2, 3}Alberto Rosso^{1}Andrea De Luca^{4}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 98 (22), 〈10.1103/PhysRevB.98.224202〉We introduce a solvable model of driven fermions that elucidates the role of the localization transition in driven disordered magnets, as used in the context of dynamic nuclear polarization. Instead of spins, we study a set of non-interacting fermions that are coupled locally to nuclear spins and tend to hyperpolarize them. The induced hyperpolarization is a fingerprint of the driven steady state of the fermions, which undergo an Anderson Localization (AL) transition upon increasing the disorder. Our central result is that the maximal hyperpolarization level is always found close to the localization transition. In the limit of small nuclear moments the maximum is pinned to the transition, and the hyperpolarization is strongly enhanced by multi-fractal correlations in the critical state of the nearly localized driven system, its magnitude reflecting multi-fractal scaling.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. PSI - Paul Scherrer Institute
- 3. ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
- 4. Rudolf Peierls Center for Theoretical Physics

## Archive ouverte HAL – Exact Persistence Exponent for the 2 D -Diffusion Equation and Related Kac Polynomials

### Mihail Poplavskyi

^{1}Gregory Schehr^{2}*Physical Review Letters*, American Physical Society, 2018, 121 (15), 〈10.1103/PhysRevLett.121.150601〉We compute the persistence for the $2d$-diffusion equation with random initial condition, i.e., the probability $p_0(t)$ that the diffusion field, at a given point ${\bf x}$ in the plane, has not changed sign up to time $t$. For large $t$, we show that $p_0(t) \sim t^{-\theta(2)}$ with $\theta(2) = 3/16$. Using the connection between the $2d$-diffusion equation and Kac random polynomials, we show that the probability $q_0(n)$ that Kac polynomials, of (even) degree $n$, have no real root decays, for large $n$, as $q_0(n) \sim n^{-3/4}$. We obtain this result by using yet another connection with the truncated orthogonal ensemble of random matrices. This allows us to compute various properties of the zero-crossings of the diffusing field, equivalently of the real roots of Kac polynomials. Finally, we unveil a precise connection with a fourth model: the semi-infinite Ising spin chain with Glauber dynamics at zero temperature.

- 1. King's College
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Entanglement evolution and generalised hydrodynamics: noninteracting systems

### Bruno BertiniMaurizio Fagotti

^{1}Lorenzo PiroliPasquale Calabrese*J.Phys.A*, 2018, 51 (39), pp.39LT01. 〈10.1088/1751-8121/aad82e〉The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement evolution after an inhomogeneous quench in noninteracting systems in the framework of generalised hydrodynamics. We focus on the protocol where two semi-infinite halves are initially prepared in different states and then joined together, showing that a proper generalisation of the quasiparticle picture leads to exact quantitative predictions. If the system is initially prepared in a quasistationary state, we find that the entanglement entropy is additive and it can be computed by means of generalised hydrodynamics. Conversely, additivity is lost when the initial state is not quasistationary; yet the entanglement entropy in the large-scale limit can be exactly predicted in the quasiparticle picture, provided that the initial state is low entangled.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Engineered Swift Equilibration for Brownian objects: from underdamped to overdamped dynamics

### Marie Chupeau

^{1}Sergio Ciliberto^{2}David Guéry-Odelin^{3}Emmanuel Trizac^{1}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2018, 20 (7), pp.075003. 〈10.1088/1367-2630/aac875〉We propose a general framework to study transformations that drive an underdamped Brownian particle in contact with a thermal bath from an equilibrium state to a new one in an arbitrarily short time. To this end, we make use of a time and space-dependent potential, that plays a dual role: confine the particle, and manipulate the system. In the special case of an isothermal compression or decompression of a harmonically trapped particle, we derive explicit protocols that perform this quick transformation, following an inverse engineering method. We focus on the properties of these protocols, which crucially depend on two key dimensionless numbers that characterize the relative values of the three timescales of the problem, associated with friction, oscillations in the confinement and duration of the protocol. In particular, we show that our protocols encompass the known overdamped version of this problem and extend it to any friction for decompression and to a large range of frictions for compression.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. Atomes Froids (LCAR)

## Archive ouverte HAL – Energy of N two-dimensional bosons with zero-range interactions

### Betzalel Bazak

^{1}Dmitry S. Petrov^{2}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2018, 20 (2), 〈10.1088/1367-2630/aaa64f〉We derive an integral equation describing $N$ two-dimensional bosons with zero-range interactions and solve it for the ground state energy $B_N$ by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go beyond the scaling $B_N\propto 8.567^N$ predicted by Hammer and Son [Phys. Rev. Lett. {\bf 93}, 250408 (2004)] in the large-$N$ limit.

- 1. IPNO - Institut de Physique Nucléaire d'Orsay
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model

### Kirill Plekhanov

^{1, 2}Ivana Vasić^{3}Alexandru Petrescu^{4}Rajbir Nirwan^{5}Guillaume Roux^{2}Walter Hofstetter^{5}Karyn Le Hur^{1}*Physical Review Letters*, American Physical Society, 2018, 120 (15), 〈10.1103/PhysRevLett.120.157201〉Recently, the frustrated XY model for spins-1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultra-cold atoms setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using the bosonic dynamical mean-field theory. Focussing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institute of Physics [Belgrade]
- 4. EE - Department of Electrical Engineering [Princeton]
- 5. ITP - Institut für Theoretische Physik [Frankfurt am Main]

## Archive ouverte HAL – Eigenstate versus Zeeman-based approaches to the solid effect

### Inés Rodríguez-Arias

^{1}Alberto Rosso^{1}Andrea De Luca^{2}*Magnetic Resonance in Chemistry*, Wiley, 2018, 56 (7), pp.689 - 698. 〈10.1002/mrc.4724〉The solid effect is one of the simplest and most effective mechanisms for Dynamic Nuclear Polarization. It involves the exchange of polarization between one electron and one nuclear spin coupled via the hyperfine interaction. Even for such a small spin system, the theoretical understanding is complicated by the contact with the lattice and the microwave irradiation. Both being weak, they can be treated within perturbation theory. In this work, we analyze the two most popular perturbation schemes: the Zeeman and the eigenstate-based approaches which differ in the way the hyperfine interaction is treated. For both schemes, we derive from first principles an effective Liouville equation which describes the density matrix of the spin system; we then study numerically the behavior of the nuclear polarization for several values of the hyperfine coupling. In general, we obtain that the Zeeman-based approach underestimates the value of the nuclear polarization. By performing a projection onto the diagonal part of the spin-system density matrix, we are able to understand the origin of the discrepancy, which is due to the presence of parasite leakage transitions appearing whenever the Zeeman basis is employed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Rudolf Peierls Centre for Theoretical Physics

## Archive ouverte HAL – Eigenfunction distribution for the Rosenzweig-Porter model

### E. Bogomolny

^{1}M. Sieber^{2}*Physical Review E*, American Physical Society (APS), 2018, 98 (3), 〈10.1103/PhysRevE.98.032139〉The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behaviour. The result is based on simple physical ideas and leads to transparent explicit formulas which agree very well with numerical calculations. It constitutes a rare case where a non-trivial eigenfunction distribution is obtained in a closed form.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. School of Mathematics [Bristol]

## Archive ouverte HAL – Effects of refractory period on stochastic resetting

### Martin R. Evans

^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018We consider a stochastic process undergoing resetting after which a random refractory period is imposed. In this period the process is quiescent and remains at the resetting position. Using a first-renewal approach, we compute exactly the stationary position distribution and analyse the emergence of a delta peak at the resetting position. In the case of a power-law distribution for the refractory period we find slow relaxation. We generalise our results to the case when the resetting period and the refractory period are correlated, by computing the Laplace transform of the survival probability of the process and the mean first passage time, i.e., the mean time to completion of a task. We also compute exactly the joint distribution of the active and absorption time to a fixed target.

- 1. SUPA, School of Physics, University of Edinburgh
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Dynamics of run-and-tumble particles in dense single-file systems

### Thibault Bertrand

^{1}Pierre Illien^{2}Olivier Benichou^{2}Raphael Voituriez^{3}#### Thibault Bertrand, Pierre Illien, Olivier Benichou, Raphael Voituriez. Dynamics of run-and-tumble particles in dense single-file systems.

*New Journal of Physics*, Institute of Physics: Open Access Journals, 2018, 20 (11), pp.113045. ⟨10.1088/1367-2630/aaef6f⟩. ⟨hal-02408409⟩- 1. Department of Mechanical Engineering and Materials Science
- 2. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Duality in Power-Law Localization in Disordered One-Dimensional Systems

### X. Deng

^{1}V. e. Kravtsov^{2, 3}G. v. Shlyapnikov^{4, 5, 6, 7, 8}L. Santos^{1}*Physical Review Letters*, American Physical Society, 2018, 120 (11), 〈10.1103/PhysRevLett.120.110602〉The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, $1/r^a$. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of $a>0$. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops ($a<1$) and short-range hops ($a>1$) in which the wave function amplitude falls off algebraically with the same power $\gamma$ from the localization center.

- 1. LUH - Leibniz Universität Hannover [Hannover]
- 2. ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
- 3. L.D. Landau Institute for Theoretical Physics of RAS
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. SPEC - UMR3680 - Service de physique de l'état condensé
- 6. Russian Quantum Center
- 7. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 8. Wuhan Institute of Physics and Mathematics

## Archive ouverte HAL – Drag force and superfluidity in the supersolid stripe phase of a spin-orbit-coupled Bose-Einstein condensate

### Giovanni I. Martone

^{1}Georgy V. Shlyapnikov^{2, 1, 3, 4, 5}*Journal of Experimental and Theoretical Physics (JETP) / Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki*, MAIK Nauka/Interperiodica, 2018The phase diagram of a spin-orbit-coupled two-component Bose gas includes a supersolid stripe phase, which is featuring density modulations along the direction of the spin-orbit coupling. This phase has been recently found experimentally [J.~Li \textit{et al.}, Nature (London) \textbf{543}, 91 (2017)]. In the present work we characterize the superfluid behavior of the stripe phase by calculating the drag force acting on a moving impurity. Because of the gapless band structure of the excitation spectrum, the Landau critical velocity vanishes if the motion is not strictly parallel to the stripes, and energy dissipation takes place at any speed. Moreover, due to the spin-orbit coupling, the drag force can develop a component perpendicular to the velocity of the impurity. Finally, by estimating the time over which the energy dissipation occurs, we find that for slow impurities the effects of friction are negligible on a time scale up to several seconds, which is comparable with the duration of a typical experiment.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 3. Russian Quantum Center
- 4. SPEC - UMR3680 - Service de physique de l'état condensé
- 5. Wuhan Institute of Physics and Mathematics

## Archive ouverte HAL – Dimer-dimer zero crossing and dilute dimerized liquid in a one-dimensional mixture

### A. Pricoupenko

^{1, 2}D. S. Petrov^{1}*Physical Review A*, American Physical Society, 2018, 97 (6), 〈10.1103/PhysRevA.97.063616〉We consider the system of dimers formed in a one-dimensional mass-balanced Bose-Bose mixture of species $\sigma=\uparrow$, $\downarrow$ with attractive interspecies and repulsive intraspecies contact interactions. In the plane parametrized by the ratios of the coupling constants $g_{\uparrow\uparrow}/|g_{\uparrow\downarrow}|$ and $g_{\downarrow\downarrow}/|g_{\uparrow\downarrow}|$ we trace out the curve where the dimer-dimer interaction switches from attractive to repulsive. We find this curve to be significantly (by more than a factor of 2) shifted towards larger $g_{\sigma\sigma}$ (or smaller $|g_{\uparrow\downarrow}|$) compared to the mean-field stability boundary $g_{\uparrow\uparrow}g_{\downarrow\downarrow}=g_{\uparrow\downarrow}^2$. For a weak dimer-dimer attraction we predict a dilute dimerized liquid phase stabilized against collapse by a repulsive three-dimer force.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. ENS Lyon - École normale supérieure - Lyon

## Archive ouverte HAL – Dimensional crossover for the beyond-mean-field correction in Bose gases

### Tobias Ilg

^{1}Jan Kumlin^{1}Luis Santos^{2}Dmitry S. Petrov^{3}Hans Peter Büchler^{1}*Physical Review A*, American Physical Society, 2018, 98 (5), 〈10.1103/PhysRevA.98.051604〉We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a box potential with periodic boundary conditions. We show that the leading contribution of the confinement-induced resonance is of beyond-mean-field order and calculate the leading corrections in the three- and low-dimensional limits. We also characterize the crossover for harmonic potentials in a model system with particularly chosen short- and long-range interactions and show the limitations of the local-density approximation. Our analysis is applicable to Bose-Bose mixtures and gives a starting point for developing the beyond-mean-field theory in inhomogeneous systems with long-range interactions such as dipolar particles or Rydberg-dressed atoms.

- 1. University of Stuttgart
- 2. LUH - Leibniz Universität Hannover [Hannover]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Deformation and flow of amorphous solids: Insights from elastoplastic models

### Alexandre Nicolas

^{1}Ezequiel E. Ferrero^{2}Kirsten Martens^{3}Jean-Louis Barrat^{3}#### Alexandre Nicolas, Ezequiel E. Ferrero, Kirsten Martens, Jean-Louis Barrat. Deformation and flow of amorphous solids: Insights from elastoplastic models.

*Reviews of Modern Physics*, American Physical Society, 2018, 90 (4), ⟨10.1103/RevModPhys.90.045006⟩. ⟨hal-02919245⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centro Atómico Bariloche [Argentine]
- 3. LIPhy [2020-….] - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] [2020-….]

## Archive ouverte HAL – Correlations of occupation numbers in the canonical ensemble and application to a Bose-Einstein condensate in a one-dimensional harmonic trap

### Olivier Giraud

^{1}Aurélien Grabsch^{1}Christophe Texier^{1}*Physical Review A*, American Physical Society, 2018, 97 (5), 〈10.1103/PhysRevA.97.053615〉We study statistical properties of $N$ non-interacting identical bosons or fermions in the canonical ensemble. We derive several general representations for the $p$-point correlation function of occupation numbers $\overline{n_1\cdots n_p}$. We demonstrate that it can be expressed as a ratio of two $p\times p$ determinants involving the (canonical) mean occupations $\overline{n_1}$, ..., $\overline{n_p}$, which can themselves be conveniently expressed in terms of the $k$-body partition functions (with $k\leq N$). We draw some connection with the theory of symmetric functions, and obtain an expression of the correlation function in terms of Schur functions. Our findings are illustrated by revisiting the problem of Bose-Einstein condensation in a 1D harmonic trap, for which we get analytical results. We get the moments of the occupation numbers and the correlation between ground state and excited state occupancies. In the temperature regime dominated by quantum correlations, the distribution of the ground state occupancy is shown to be a truncated Gumbel law. The Gumbel law, describing extreme value statistics, is obtained when the temperature is much smaller than the Bose-Einstein temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Collective Spin Modes of a Trapped Quantum Ferrofluid

### S. Lepoutre

^{1}L. GabardosK. KechadiP. Pedri^{2}O. Gorceix^{1}E. Maréchal^{3}L. Vernac^{1}B. Laburthe-Tolra^{1}*Physical Review Letters*, American Physical Society, 2018, 121 (1)- 1. LPL - Laboratoire de Physique des Lasers
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. inconnu

## Archive ouverte HAL – Cell contraction induces long-ranged stress stiffening in the extracellular matrix

### Yu Long Han

^{1}Pierre Ronceray^{2}Guoqiang Xu^{1}Andrea Malandrino^{3, 1}Roger Kamm^{1}Martin Lenz^{4}Chase P. Broedersz^{5}Ming Guo^{1}*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2018Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing Nonlinear Stress Inference Microscopy (NSIM), a novel technique to infer stress fields in a 3D matrix from nonlinear microrheology measurement with optical tweezers. Using NSIM and simulations, we reveal a long-ranged propagation of cell-generated stresses resulting from local filament buckling. This slow decay of stress gives rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which could form a mechanism for mechanical communication between cells.

- 1. MIT - Massachusetts Institute of Technology
- 2. Princeton Center for Theoretical Science
- 3. IBEC - Institute for Bioengineering of Catalonia [Barcelona]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Ludwig-Maximilians-Universität München

## Archive ouverte HAL – Building blocks of topological quantum chemistry: Elementary band representations

### Jennifer Cano

^{1}Barry Bradlyn^{1}Zhijun Wang^{1}L. Elcoro^{2}M. G. Vergniory^{2}C. Felser^{3}M. I. Aroyo^{2}B. Andrei Bernevig^{4, 5, 6}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 97 (3), 〈10.1103/PhysRevB.97.035139〉The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of "elementary" band representations. In Nature 547, 298-305 (2017), we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here, we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time-reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wavefunctions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, which we introduced in Nature 547, 298-305 (2017), we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. University of the Basque Country - University of the Basque Country
- 3. CPfS - Max Planck Institute for Chemical Physics of Solids
- 4. DPPU - Department of Physics,Princeton University
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Band connectivity for topological quantum chemistry: Band structures as a graph theory problem

### Barry Bradlyn

^{1}L. Elcoro^{2}M. G. Vergniory^{2}Jennifer Cano^{1}Zhijun Wang^{1}C. Felser^{3}M. I. Aroyo^{2}B. Andrei Bernevig^{4, 5, 6}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 97 (3), 〈10.1103/PhysRevB.97.035138〉The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature 547, 298 (2017)], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local "k-dot-p" band structures across the Brillouin zone in terms of graph theory. In the current manuscript we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph-theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. University of the Basque Country - University of the Basque Country
- 3. CPfS - Max Planck Institute for Chemical Physics of Solids
- 4. DPPU - Department of Physics,Princeton University
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Asymptotics for the expected maximum of random walks and Lévy flights with a constant drift

### Philippe Mounaix

^{1}Satya Majumdar^{2}Gregory Schehr^{2}#### Philippe Mounaix, Satya Majumdar, Gregory Schehr. Asymptotics for the expected maximum of random walks and Lévy flights with a constant drift.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2018, 2018 (8), pp.083201. ⟨10.1088/1742-5468/aad364⟩. ⟨hal-02325419⟩- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Active Mechanics Reveal Molecular-Scale Force Kinetics in Living Oocytes

### Wylie AhmedEtienne Fodor

^{1}Maria Almonacid^{2}Matthias BussonnierMarie-Hélène Verlhac^{2}Nir Gov^{3}Paolo Visco^{4}Frédéric van Wijland^{1}Timo Betz^{5}#### Wylie Ahmed, Etienne Fodor, Maria Almonacid, Matthias Bussonnier, Marie-Hélène Verlhac, et al.. Active Mechanics Reveal Molecular-Scale Force Kinetics in Living Oocytes.

*Biophysical Journal*, Biophysical Society, 2018, 114 (7), pp.1667-1679. ⟨10.1016/j.bpj.2018.02.009⟩. ⟨hal-02379042⟩- 1. MSC (UMR_7057) - Matière et Systèmes Complexes
- 2. CIRB - Centre interdisciplinaire de recherche en biologie
- 3. Institut Weizmann
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. WWU - Westfälische Wilhelms-Universität Münster

## Archive ouverte HAL – Active Brownian motion in two dimensions

### Urna Basu

^{1}Satya N. Majumdar^{2}Alberto Rosso^{2}Satya Majumdar^{2}Gregory Schehr^{2}*Physical Review E*, American Physical Society (APS), 2018, 98 (6), 〈10.1103/PhysRevE.98.062121〉We study the dynamics of a single active Brownian particle (ABP) in a two-dimensional harmonic trap. The active particle has an intrinsic time scale $D_R^{-1}$ set by the rotational diffusion with diffusion constant $D_R$. The harmonic trap also induces a relaxational time-scale $\mu^{-1}$. We show that the competition between these two time scales leads to a nontrivial time evolution for the ABP. At short times a strongly anisotropic motion emerges leading to anomalous persistence/first-passage properties. At long-times, the stationary position distribution in the trap exhibits two different behaviours: a Gaussian peak at the origin in the strongly passive limit ($D_R \to \infty$) and a delocalised ring away from the origin in the opposite strongly active limit ($D_R \to 0$). The predicted stationary behaviours in these limits are in agreement with recent experimental observations.

- 1. Theoretical Condensed Matter Physics Division
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – A Trap Model for Clogging and Unclogging in Granular Hopper Flows

### Alexandre Nicolas

^{1}Angel Garcimartín^{2}Iker Zuriguel^{2}*Physical Review Letters*, American Physical Society, 2018, 120 (19), pp.198002. 〈https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.198002〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. UNAV - Universidad de Navarra [Pamplona]

## Archive ouverte HAL – A nonequilibrium force can stabilize 2D active nematics

### Ananyo Maitra

^{1, *}Pragya Srivastava^{2}M. Cristina Marchetti^{3}Juho Lintuvuori^{4}Sriram Ramaswamy^{5, 6}Martin Lenz^{1, 7, *}*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2018, 115 (27), pp.6934-6939Suspensions of actively driven anisotropic objects exhibit distinctively nonequilibrium behaviors, and current theories predict that they are incapable of sustaining orientational order at high activity. By contrast, here we show that nematic suspensions on a substrate can display order at arbitrarily high activity due to a previously unreported, potentially stabilizing active force. This force moreover emerges inevitably in theories of active orientable fluids under geometric confinement. The resulting nonequilibrium ordered phase displays robust giant number fluctuations that cannot be suppressed even by an incompressible solvent. Our results apply to virtually all experimental assays used to investigate the active nematic ordering of self-propelled colloids, bacterial sus-pensions, and the cytoskeleton and have testable implications in interpreting their nonequilibrium behaviors.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Theoretical Physics of Biology Laboratory
- 3. Department of Physics [Syracuse]
- 4. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 5. TIFR - Tata Institute of Fundamental Research [Hyderabad]
- 6. Centre for Condensed Matter Theory [Bangalore]
- 7. MSE2 - Multiscale Materials Science for Energy and Environment

## Archive ouverte HAL – A Minimal Power Model for Human Running Performance

### Matthew Mulligan

^{1}Guillaume Adam^{2}Thorsten Emig^{3, 4}*PLoS ONE*, Public Library of Science, 2018Models for human running performances of various complexities and underlying principles have been proposed, often combining data from world record performances and bio-energetic facts of human physiology. Here we present a novel, minimal and universal model for human running performance that employs a relative metabolic power scale. The main component is a self-consistency relation for the time dependent maximal power output. The analytic approach presented here is the first to derive the observed logarithmic scaling between world (and other) record running speeds and times from basic principles of metabolic power supply. Various female and male record performances (world, national) and also personal best performances of individual runners for distances from 800m to the marathon are excellently described by this model, with mean errors of (often much) less than 1%. The model defines endurance in a way that demonstrates symmetry between long and short racing events that are separated by a characteristic time scale comparable to the time over which a runner can sustain maximal oxygen uptake. As an application of our model, we derive personalized characteristic race speeds for different durations and distances.

- 1. Claremont Mckenna College - CMC (USA)
- 2. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment
- 3. MIT - Massachusetts Institute of Technology
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – A counterintuitive way to speed up pedestrian and granular bottleneck flows prone to clogging: Can ‘more’ escape faster?

### Alexandre Nicolas

^{1}Santiago Ibáñez^{2}Marcelo Kuperman^{2}Sebastián Bouzat^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018, 2018 (8), pp.083403. 〈http://iopscience.iop.org/article/10.1088/1742-5468/aad6c0〉Dense granular flows through constrictions, as well as competitive pedestrian evacuations, are hindered by a propensity to form clogs. We use simulations of model pedestrians and experiments with granular disks to explore an original strategy to speed up these flows, which consists in including contact-averse entities in the assembly. On the basis of a minimal cellular automaton and a continuous agent-based model for pedestrian evacuation dynamics, we find that the inclusion of polite pedestrians amid a given competitive crowd fails to reduce the evacuation time when the constriction (the doorway) is acceptably large. This is not surprising, because adding agents makes the crowd larger. In contrast, when the door is so narrow that it can accommodate at most one or two agents at a time, our strategy succeeds in substantially curbing long-lived clogs and speeding up the evacuation. A similar effect is seen experimentally in a vibrated two-dimensional hopper flow with an opening narrower than 3 disk diameters. Indeed, by adding to the initial collection of neutral disks a large fraction of magnetic ones, interacting repulsively, we observe a shortening of the time intervals between successive egresses of neutral disks, as reflected by the study of their probability distribution. On a more qualitative note, our study suggests that the much discussed analogy between pedestrian flows and granular flows could be extended to some behavioural traits of individual pedestrians.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centro Atómico Bariloche [Argentine]

## Archive ouverte HAL – A correlation-hole approach to the electric double layer with counter-ions only

### Ivan Palaia

^{1}Martin Trulsson^{2}L. Samaj^{3}Emmanuel Trizac^{1}Ladislav Šamaj^{3}*Molecular Physics*, Taylor & Francis, 2018, 116 (21-22), pp.3134 - 3146. 〈10.1080/00268976.2018.1471234〉We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new self-consistent theory of the correlation-hole type is proposed which leads to a modified Poisson-Boltzmann integral equation for the density profile, convenient for analytical progress and straightforward to solve numerically. The exact density profiles are recovered in the limits of weak and strong couplings. In contrast to previous theoretical attempts of the test-charge family, the density profiles fulfill the contact-value theorem at all values of the coupling constant, and exhibit the mean-field decay at asymptotically large distances from the wall, as expected. We furthermore show that the density corrections at large couplings exhibit the proper dependence on coupling parameter and distance to the charged wall. The numerical results for intermediate values of the coupling provide accurate density profiles which are in good agreement with those obtained by Monte-Carlo simulations. The crossover to mean-field behavior at large distance is studied in detail.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Lund University [Lund]
- 3. Institute of Physics

## A Trap Model for Clogging and Unclogging in Granular Hopper Flows

### Alexandre Nicolas

^{1}Angel Garcimartín^{2}Iker Zuriguel^{2}*Physical Review Letters*, American Physical Society, 2018, 120 (19), pp.198002. 〈https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.198002〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. UNAV - Universidad de Navarra [Pamplona]

## What drives transient behavior in complex systems?

### Jacek Grela

^{1}*Phys.Rev.E*, 2017, 96 (2), pp.022316. 〈10.1103/PhysRevE.96.022316〉We study transient behavior in the dynamics of complex systems described by a set of nonlinear ordinary differential equations. Destabilizing nature of transient trajectories is discussed and its connection with the eigenvalue-based linearization procedure. The complexity is realized as a random matrix drawn from a modified May-Wigner model. Based on the initial response of the system, we identify a novel stable-transient regime. We calculate exact abundances of typical and extreme transient trajectories finding both Gaussian and Tracy-Widom distributions known in extreme value statistics. We identify degrees of freedom driving transient behavior as connected to the eigenvectors and encoded in a nonorthogonality matrix T0. We accordingly extend the May-Wigner model to contain a phase with typical transient trajectories present. An exact norm of the trajectory is obtained in the vanishing T0 limit where it describes a normal matrix.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

### Pierfrancesco Urbani

^{1}Francesco Zamponi^{2}Silvio Franz^{3}Giorgio Parisi^{4}Maksim Sevelev^{3}*SciPost Physics*, 2017, 2 (3), pp.019Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been studied often involve discrete degrees of freedom: standard random CSPs are random K-SAT (aka disordered Ising models) or random coloring problems (aka disordered Potts models). In this work we consider instead problems that involve continuous degrees of freedom. The simplest prototype of these problems is the perceptron. Here we discuss in detail the full phase diagram of the model. In the regions of parameter space where the problem is non-convex, leading to multiple disconnected clusters of solutions, the solution is critical at the SAT/UNSAT threshold and lies in the same universality class of the jamming transition of soft spheres. We show how the critical behavior at the satisfiability threshold emerges, and we compute the critical exponents associated to the approach to the transition from both the SAT and UNSAT phase. We conjecture that there is a large universality class of non-convex continuous CSPs whose SAT-UNSAT threshold is described by the same scaling solution.

- 1. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Dipartimento di Fisica [Roma]

## Two-body relaxation of spin-polarized fermions in reduced dimensionalities near a p-wave Feshbach resonance

### D. V. Kurlov

^{1}G. V. Shlyapnikov^{2}*Physical Review A*, American Physical Society, 2017, 95 (3), pp.032710We study inelastic two-body relaxation in a spin-polarized ultracold Fermi gas in the presence of a p-wave Feshbach resonance. It is shown that in reduced dimensionalities, especially in the quasi-one-dimensional case, the enhancement of the inelastic rate constant on approach to the resonance is strongly suppressed compared to three dimensions. This may open promising paths for obtaining novel many-body states.

- 1. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Two- and three-body problem with Floquet-driven zero-range interactions

### A. G. Sykes

^{1}H. Landa^{1}D. S. Petrov^{1}*Physical Review A*, American Physical Society, 2017, 95 (6), pp.062705We study the two-body scattering problem in the zero-range approximation with a sinusoidally driven scattering length and calculate the relation between the mean value and amplitude of the drive for which the effective scattering amplitude is resonantly enhanced. In this manner we arrive at a family of curves along which the effective scattering length diverges but the nature of the corresponding Floquet-induced resonance changes from narrow to wide. Remarkably, on these curves the driving does not induce heating. In order to study the effect of these resonances on the three-body problem we consider one light and two heavy particles with driven heavy-light interaction in the Born-Oppenheimer approximation and find that the Floquet driving can be used to tune the three-body and inelasticity parameters.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Truncated linear statistics associated with the top eigenvalues of random matrices

### Aurélien Grabsch

^{1}Satya N. Majumdar^{1}Christophe Texier^{1}*Journal of Statistical Physics*, Springer Verlag, 2017, 167 (2), pp.234 - 259Given a certain invariant random matrix ensemble characterised by the joint probability distribution of eigenvalues $P(\lambda_1,\cdots,\lambda_N)$, many important questions have been related to the study of linear statistics of eigenvalues $L=\sum_{i=1}^Nf(\lambda_i)$, where $f(\lambda)$ is a known function. We study here truncated linear statistics where the sum is restricted to the $N_1

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Truncated linear statistics associated with the eigenvalues of random matrices II. Partial sums over proper time delays for chaotic quantum dots

### Aurélien Grabsch

^{1}Satya N. Majumdar^{1}Christophe Texier^{1}*Journal of Statistical Physics*, Springer Verlag, 2017, 167 (6), pp.1452 - 1488Invariant ensembles of random matrices are characterized by the distribution of their eigenvalues $\{\lambda_1,\cdots,\lambda_N\}$. We study the distribution of truncated linear statistics of the form $\tilde{L}=\sum_{i=1}^p f(\lambda_i)$ with $p

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Three-dimensional resistivity switching between correlated electronic states in 1T-TaS2

### Damjan Svetin

^{1}Igor Vaskivskyi^{2}Serguei Brazovskii^{3}Dragan Mihailovic^{4, 1, 2}*Scientific Reports*, Nature Publishing Group, 2017, 7, pp.46048Recent demonstrations of controlled switching between different ordered macroscopic states by impulsive electromagnetic perturbations in complex materials have opened some fundamental questions on the mechanisms responsible for such remarkable behavior. Here we experimentally address the question of whether two-dimensional (2D) Mott physics can be responsible for unusual switching between states of different electronic order in the layered dichalcogenide 1T-TaS2, or it is a result of subtle inter-layer orbitronic re-ordering of its helical stacking structure. We report on the switching properties both in-plane and perpendicular to the layers by current-pulse injection, the anisotropy of electronic transport in the commensurate ground state, and relaxation properties of the switched metastable state. Contrary to recent theoretical calculations, which predict a uni-directional metal perpendicular to the layers, we observe a large resistivity in this direction, with a temperature-dependent anisotropy. Remarkably, large resistance ratios are observed in the memristive switching both in-plane (IP) and out-of-plane (OP). The relaxation dynamics of the metastable state for both IP and OP electron transport are seemingly governed by the same mesoscopic quantum re-ordering process. We conclude that 1T-TaS2 shows resistance switching arising from an interplay of both IP and OP correlations.

- 1. Department of Complex Matter
- 2. University of Ljubljana
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. CENN Nanocenter

## The open XXX spin chain in the SoV framework: scalar product of separate states

### Nikolai Kitanine

^{1, *}Jean-Michel Maillet^{2}Giuliano Niccoli^{2}Véronique Terras^{3}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2017, 50 (22), pp.224001. 〈10.1088/1751-8121/aa6cc9〉We consider the XXX open spin-1/2 chain with the most general non-diagonal boundary terms, that we solve by means of the quantum separation of variables (SoV) approach. We compute the scalar products of separate states, a class of states which notably contains all the eigenstates of the model. As usual for models solved by SoV, these scalar products can be expressed as some determinants with a non-trivial dependance in terms of the inhomogeneity parameters that have to be introduced for the method to be applicable. We show that these determinants can be transformed into alternative ones in which the homogeneous limit can easily be taken. These new representations can be considered as generalizations of the well-known determinant representation for the scalar products of the Bethe states of the periodic chain. In the particular case where a constraint is applied on the boundary parameters, such that the transfer matrix spectrum and eigenstates can be characterized in terms of polynomial solutions of a usual T-Q equation, the scalar product that we compute here corresponds to the scalar product between two off-shell Bethe-type states. If in addition one of the states is an eigenstate, the determinant representation can be simplified, hence leading in this boundary case to direct analogues of algebraic Bethe ansatz determinant representations of the scalar products for the periodic chain.

- 1. IMB - Institut de Mathématiques de Bourgogne [Dijon]
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Temperature Distribution and Heat Radiation of Patterned Surfaces at Short Wave Lengths

### Thorsten Emig

^{1, 2}*Physical Review E*, American Physical Society (APS), 2017, 95 (5), pp.052104We analyze the equilibrium spatial distribution of surface temperatures of patterned surfaces. The surface is exposed to a constant external heat flux and has a fixed internal temperature that is coupled to the outside heat fluxes by finite heat conductivity across surface. It is assumed that the temperatures are sufficiently high so that the thermal wavelength (a few microns at room temperature) is short compared to all geometric length scales of the surface patterns. Hence the radiosity method can be employed. A recursive multiple scattering method is developed that enables rapid convergence to equilibrium temperatures. While the temperature distributions show distinct dependence on the detailed surface shapes (cuboids and cylinder are studied), we demonstrate robust universal relations between the mean and the standard deviation of the temperature distributions and quantities that characterize overall geometric features of the surface shape.

- 1. MIT - Massachusetts Institute of Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Survival probability of random walks and Lévy flights on a semi-infinite line

### Satya N. Majumdar

^{1}Philippe Mounaix^{2}Gregory Schehr^{1}Satya Majumdar^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2017, 50 (46), 〈10.1088/1751-8121/aa8d28〉We consider a one-dimensional random walk (RW) with a continuous and symmetric jump distribution, $f(\eta)$, characterized by a L\'evy index $\mu \in (0,2]$, which includes standard random walks ($\mu=2$) and L\'evy flights ($0<\mu<2$). We study the survival probability, $q(x_0,n)$, representing the probability that the RW stays non-negative up to step $n$, starting initially at $x_0 \geq 0$. Our main focus is on the $x_0$-dependence of $q(x_0,n)$ for large $n$. We show that $q(x_0,n)$ displays two distinct regimes as $x_0$ varies: (i) for $x_0= O(1)$ ("quantum regime"), the discreteness of the jump process significantly alters the standard scaling behavior of $q(x_0,n)$ and (ii) for $x_0 = O(n^{1/\mu})$ ("classical regime") the discrete-time nature of the process is irrelevant and one recovers the standard scaling behavior (for $\mu =2$ this corresponds to the standard Brownian scaling limit). The purpose of this paper is to study how precisely the crossover in $q(x_0,n)$ occurs between the quantum and the classical regime as one increases $x_0$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CPHT - Centre de Physique Théorique [Palaiseau]

## Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya. N. Majumdar^{3}Gregory Schehr^{3, *}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017, 2017 (6), pp.063301 (1-39). 〈10.1088/1742-5468/aa6dda〉We consider N non-interacting fermions in an isotropic d-dimensional harmonic trap. We compute analytically the cumulative distribution of the maximal radial distance of the fermions from the trap center at zero temperature. While in d = 1 the limiting distribution (in the large N limit), properly centered and scaled, converges to the squared Tracy–Widom distribution of the Gaussian unitary ensemble in random matrix theory, we show that for all d > 1, the limiting distribution converges to the Gumbel law. These limiting forms turn out to be universal, i.e. independent of the details of the trapping potential for a large class of isotropic trapping potentials. We also study the position of the right-most fermion in a given direction in d dimensions and, in the case of a harmonic trap, the maximum momentum, and show that they obey similar Gumbel statistics. Finally, we generalize these results to low but finite temperature.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Statistics of fermions in a d-dimensional box near a hard wall

### Bertrand Lacroix-A-Chez-Toine

^{1}Pierre Le Doussal^{2}Satya Majumdar^{1}Grégory Schehr^{1}*EPL*, 2017, 120 (1), pp.10006. 〈10.1209/0295-5075/120/10006〉We study N noninteracting fermions in a domain bounded by a hard-wall potential in dimensions. We show that for large N, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth confining potentials. We compute this d-dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any sufficiently smooth boundary. As an application we compute the quantum statistics of the position of the fermion closest to the hard wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Statistics of fermions in a $d$-dimensional box near a hard wall

### Bertrand Lacroix-A-Chez-Toine

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Gregory Schehr^{1}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017We study $N$ noninteracting fermions in a domain bounded by a hard wall potential in $d \geq 1$ dimensions. We show that for large $N$, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth potentials. We compute this $d$ dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any sufficiently smooth boundary. As an application we compute the quantum statistics of the position of the fermion closest to the wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Spectroscopy and Directed Transport of Topological Solitons in Crystals of Trapped Ions

### J. Brox

^{1}P. Kiefer^{1}M. Bujak^{1}H. Landa^{2}T. Schaetz^{1}*Physical Review Letters*, American Physical Society, 2017, 119 (15), 〈10.1103/PhysRevLett.119.153602〉We study experimentally and theoretically discrete solitons in crystalline structures consisting of several tens of laser-cooled ions confined in a radiofrequency trap. Resonantly exciting localized, spectrally gapped vibrational modes of the soliton, a nonlinear mechanism leads to a nonequilibrium steady state of the continuously cooled crystal. We find that the propagation and the escape of the soliton out of its a quasi-one-dimensional channel can be described as a thermal activation mechanism. We control the effective temperature of the soliton's collective coordinate by the amplitude of the external excitation. Furthermore, the global trapping potential permits controlling the soliton dynamics and realizing directed transport depending on its topological charge.

- 1. Albert-Ludwigs-Universität Freiburg
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Spatio-temporal patterns in ultra-slow domain wall creep dynamics

### Ezequiel E. Ferrero

^{1}Laura Foini^{2}Thierry Giamarchi^{2}Alejandro B. Kolton^{3}Alberto Rosso^{4}*Physical Review Letters*, American Physical Society, 2017, 118 (14), pp.147208In presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps, called avalanches, while, at much smaller field, these interfaces creep by thermal activation. In this work we develop a novel numerical technique that captures the ultra-slow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatio-temporal patterns that resemble the complex sequence of aftershocks observed after a large earthquake. Remarkably, we show that events assembly in independent clusters that display at large scales the same statistics as critical depinning avalanches. We foresee this correlated dynamics being experimentally accessible by magneto-optical imaging of ferromagnetic films.

- 1. LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
- 2. Department of Quantum Matter Physics
- 3. CONICET Centro Atomico Bariloche
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

### S. K. Ivanov

^{1, 2}A. M. Kamchatnov^{3, 1}T. Congy^{4}N. Pavloff^{4}*Physical Review E*, American Physical Society (APS), 2017, 96 (6), 〈10.1103/PhysRevE.96.062202〉We provide a classification of the possible flow of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferro-magnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as to the appearance of new elements --- contact dispersive shock waves --- that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

- 1. MIPT - Moscow Institute of Physics and Technology [Moscow]
- 2. Institute of Spectroscopy of the RAS
- 3. Institute of Spectroscopy
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Shape of the magnetoroton at $\nu=1/3$ and $\nu=7/3$ in real samples

### Thierry Jolicoeur

^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95, pp.075201We revisit the theory of the collective neutral excitation mode in the fractional quantum Hall effect at Landau level filling fractions $\nu=1/3$ and $\nu=7/3$. We include the effect of finite thickness of the two-dimensional electron gas and use extensive exact diagonalizations in the torus geometry. In the lowest Landau level the collective gapped mode i.e. the magnetoroton always merges in the continuum in the long-wavelength limit. In the second Landau level the mode is well-defined only for wavevectors smaller than a critical value and disappears in the continuum beyond this point. Its curvature near zero momentum is opposite to that of the LLL. It is well separated from the continuum even at zero momentum and the gap of the continuum of higher-lying states is twice the collective mode gap at $k=0$. The shape of the dispersion relation survives a perturbative treatment of Landau level mixing.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation

### Vladimir Belavin

^{1, 2}Xiangyu Cao^{3}Benoit Estienne^{4}Raoul Santachiara^{3}*Journal of High Energy Physics*, Springer, 2017, 3, pp.008In a recent study we considered W3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl3. We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

- 1. P. N. Lebedev Physical Institute of the Russian Academy of Sciences
- 2. IITP - Institute for Information Transmission Problems
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. LPTHE - Laboratoire de Physique Théorique et Hautes Energies

## Search in Patchy Media: Exploration-Exploitation Tradeoff

### M. Chupeau

^{1, 2}O. Bénichou^{2}S. Redner^{3, 4}*Physical Review E*, American Physical Society (APS), 2017, 95 (1), pp.012157How to best exploit patchy resources? This long-standing question belongs to the extensively studied class of explore/exploit problems that arise in a wide range of situations, from animal foraging, to robotic exploration, and to human decision processes. Despite its broad relevance, the issue of optimal exploitation has previously only been tackled through two paradigmatic limiting models---patch-use and random search---that do not account for the interplay between searcher motion within patches and resource depletion. Here, we bridge this gap by introducing a minimal patch exploitation model that incorporates this coupling: the searcher depletes the resources along its random-walk trajectory within a patch and travels to a new patch after it takes $\mathcal{S}$ consecutive steps without finding resources. We compute the distribution of the amount of resources $F_t$ consumed by time $t$ for this non-Markovian random walker and show that exploring multiple patches is beneficial. In one dimension, we analytically derive the optimal strategy to maximize $F_t$. We show that this strategy is robust with respect to the distribution of resources within patches and the criterion for leaving a given patch. We also show that $F_t$ can be optimized in the ecologically-relevant case of two-dimensional patchy environments.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
- 3. BU - Boston University [Boston]
- 4. Santa Fe Institute

## Scaling Description of Non-Local Rheology

### Thomas Gueudré

^{1}Jie Lin^{2}Alberto Rosso^{3}Matthieu Wyart^{4}*Soft Matter*, Royal Society of Chemistry, 2017, 13, pp.3794Non-locality is crucial to understand the plastic flow of an amorphous material, and has been successfully described by the fluidity, along with a cooperativity length scale {\xi}. We demonstrate, by applying the scaling hypothesis to the yielding transition, that non-local effects in non-uniform stress configurations can be explained within the framework of critical phenomena. From the scaling description, scaling relations between different exponents are derived, and collapses of strain rate profiles are made both in shear driven and pressure driven flow. We find that the cooperative length in non-local flow is governed by the same correlation length in finite dimensional homogeneous flow, excluding the mean field exponents. We also show that non-locality also affects the finite size scaling of the yield stress, especially the large finite size effects observed in pressure driven flow. Our theoretical results are nicely verified by the elasto-plastic model, and experimental data.

- 1. Polito - Politecnico di Torino [Torino]
- 2. DEPARTMENT OF PHYSICS - New York University
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Institute of Theoretical Physics, Ecole Polytechnique Fédérale, de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

## Regularly Decomposable Tensors and Classical Spin States

### Liqun Qi

^{1}Guofeng Zhang^{1}Daniel Braun^{2}Fabian Bohnet-Waldraff^{3, 2}Olivier Giraud^{3}*Communications in Mathematical Sciences*, International Press, 2017, 15, pp.1651A spin-$j$ state can be represented by a symmetric tensor of order $N=2j$ and dimension $4$. Here, $j$ can be a positive integer, which corresponds to a boson; $j$ can also be a positive half-integer, which corresponds to a fermion. In this paper, we introduce regularly decomposable tensors and show that a spin-$j$ state is classical if and only if its representing tensor is a regularly decomposable tensor. In the even-order case, a regularly decomposable tensor is a completely decomposable tensor but not vice versa; a completely decomposable tensors is a sum-of-squares (SOS) tensor but not vice versa; an SOS tensor is a positive semi-definite (PSD) tensor but not vice versa. In the odd-order case, the first row tensor of a regularly decomposable tensor is regularly decomposable and its other row tensors are induced by the regular decomposition of its first row tensor. We also show that complete decomposability and regular decomposability are invariant under orthogonal transformations, and that the completely decomposable tensor cone and the regularly decomposable tensor cone are closed convex cones. Furthermore, in the even-order case, the completely decomposable tensor cone and the PSD tensor cone are dual to each other. The Hadamard product of two completely decomposable tensors is still a completely decomposable tensor. Since one may apply the positive semi-definite programming algorithm to detect whether a symmetric tensor is an SOS tensor or not, this gives a checkable necessary condition for classicality of a spin-$j$ state. Further research issues on regularly decomposable tensors are also raised.

- 1. POLYU - The Hong Kong Polytechnic University [Hong Kong]
- 2. Institut für Physikalische und Theoretische Chemie, Universität Tübingen, Tübingen
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Quasi-universality in mixed salt-free counterions systems

### M. Trulsson

^{1}Ladislav Šamaj^{2}E. Trizac^{1}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017, 118 (1), pp.16001The screening of plate-plate interactions by counterions is an age-old problem. We revisit this classic question when counterions exhibit a distribution of charges. While it is expected that the long-distance regime of interactions is universal, the behaviour of the inter-plate pressure at smaller distances should a priori depend rather severely on the nature of the ionic mixture screening the plate charges. We show that is not the case, and that for comparable Coulombic couplings, different systems exhibit a quasi-universal equation of state.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. INSTITUTE OF PHYSICS - SLOVAK ACADEMY OF SCIENCES Institute of Physics Dubraska cesta 9, 84228 Bratislava, Slovaquie

## Quantum quenches with random matrix Hamiltonians and disordered potentials

### Fabian Kolley

^{1}Oriol Bohigas^{2}Boris V. Fine^{1, 3}*Annalen der Physik*, 2017We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists of sudden switching-on the off-diagonal elements of the Hamiltonian. In the latter case, it is sudden switching-on of the hopping between adjacent lattice sites. The quench-induced ensembles are compared with the so-called "quantum micro-canonical" (QMC) ensemble describing quantum superpositions with fixed energy expectation values. Our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the QMC ensemble. Away from the QMC condensation regime, the overall agreement with the QMC predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate.

- 1. University of Heidelberg
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Skoltech - Skolkovo Institute of Science and Technology [Moscow]

## Quantum Phases and Collective Excitations of a Spin-Orbit-Coupled Bose–Einstein Condensate in a One-Dimensional Optical Lattice

### G. Martone

^{1}*Journal of Low Temperature Physics*, Springer Verlag (Germany), 2017, 189 (5-6), pp.262 - 275. 〈10.1007/s10909-017-1816-9〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Quantum Ising model in transverse and longitudinal fields: chaotic wave functions

### Y. Y. Atas

^{1}E. Bogomolny^{2}*Journal of Physics A: Mathematical and General*, IOP Publishing, 2017, 50, pp.385102The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal fields is discussed in detail for the chaotic case. When the number of spins is large, each wave function coefficient has the Gaussian distribution with zero mean and the variance calculated from the first two moments of the Hamiltonian. The main part of the paper is devoted to the discussion of different corrections to the asymptotic result. One type of corrections is related with higher order moments of the Hamiltonian and can be taken into account by Gibbs-like formulae. Another corrections are due to symmetry contributions which manifest as different numbers of non-zero real and complex coefficients. Statistical model with these corrections included agrees well with numerical calculations of wave function moments.

- 1. School of Mathematics and Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Quand le squelette des cellules produit des forces

### Martin Lenz

^{1}*médecine/sciences*, EDP Sciences, 2017, 33 (2), pp.121 - 123. 〈10.1051/medsci/20173302002〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

### Trithep Devakul

^{1}Satya N. Majumdar^{2}David A. Huse^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95 (10), pp.104204We calculate the probability distribution of entanglement entropy S across a cut of a finite one dimensional spin chain of length L at an infinite randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form $p(S|L) \sim L^{-\psi(k)}$, where $k = S / \log [L/L_0]$, the large deviation function $\psi(k)$ is found explicitly, and $L_0$ is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix product state (MPS) based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

- 1. DPPU - Department of Physics,Princeton University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

### Alexandru Petrescu

^{1}Marie Piraud^{2}Guillaume Roux^{3}I. P. Mcculloch^{4}Karyn Le Hur^{5}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 96 (1), pp.014524. 〈10.1103/PhysRevB.96.014524〉- 1. EE - Department of Electrical Engineering [Princeton]
- 2. Department of Physics and Arnold Sommerfeld Center for Theoretical Physics
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. ARC Centre for Engineered Quantum Systems
- 5. CPHT - Centre de Physique Théorique [Palaiseau]

## Pickands’ constant at first order in an expansion around Brownian motion

### Mathieu Delorme

^{1}Alberto Rosso^{2}Kay Jörg Wiese^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2017, 50, pp.16LT04In the theory of extreme values of Gaussian processes, many results are expressed in terms of the Pickands constant $\mathcal{H}_{\alpha}$. This constant depends on the local self-similarity exponent $\alpha$ of the process, i.e. locally it is a fractional Brownian motion (fBm) of Hurst index $H=\alpha/2$. Despite its importance, only two values of the Pickands constant are known: ${\cal H}_1 =1$ and ${\cal H}_2=1/\sqrt{\pi}$. Here, we extend the recent perturbative approach to fBm to include drift terms. This allows us to investigate the Pickands constant $\mathcal{H}_{\alpha}$ around standard Brownian motion ($\alpha =1$) and to derive the new exact result $\mathcal{H}_{\alpha}=1 - (\alpha-1) \gamma_{\rm E} + \mathcal{O}\!\left( \alpha-1\right)^{2}$.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps

### Thiago M. SchlittlerRémy Mosseri

^{1}Thomas Barthel^{2, 3}Thiago Schlittler^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 96 (19), 〈10.1103/PhysRevB.96.195142〉The phase diagram of the quantum dimer model on the hexagonal (honeycomb) lattice is computed numerically, extending on earlier work by Moessner, Sondhi, and Chandra. The different ground state phases are studied in detail using several local and global observables. In addition, we analyze imaginary-time correlation functions to determine ground state energies as well as gaps to the first excited states. This leads in particular to a confirmation that the intermediary so-called plaquette phase is gapped -- a point which was previously advocated with general arguments and some data for an order parameter, but required a more direct proof. On the technical side, we describe an efficient world-line quantum Monte Carlo algorithm with improved cluster updates that increase acceptance probabilities by taking account of potential terms of the Hamiltonian during the cluster construction. The Monte Carlo simulations are supplemented with variational computations.

- 1. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Duke university [Durham]

## Periodic Airy process and equilibrium dynamics of edge fermions in a trap

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}*Annals of Physics*, 2017, 383, pp.312 - 345We establish an exact mapping between (i) the equilibrium (imaginary time) dynamics of non-interacting fermions trapped in a harmonic potential at temperature $T=1/\beta$ and (ii) non-intersecting Ornstein-Uhlenbeck (OU) particles constrained to return to their initial positions after time $\beta$. Exploiting the determinantal structure of the process we compute the universal correlation functions both in the bulk and at the edge of the trapped Fermi gas. The latter corresponds to the top path of the non-intersecting OU particles, and leads us to introduce and study the time-periodic Airy$_2$ process, ${\cal A}^b_2(u)$, depending on a single parameter, the period $b$. The standard Airy$_2$ process is recovered for $b=+\infty$. We discuss applications of our results to the real time quantum dynamics of trapped fermions.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Pedestrian flows through a narrow doorway: Effect of individual behaviours on the global flow and microscopic dynamics

### Alexandre Nicolas

^{1, 2}Sebastián Bouzat^{2}Marcelo Kuperman^{3, 2}*Transportation Research Part B: Methodological*, Elsevier, 2017We study the dynamics of pedestrian evacuations through a narrow doorway by means of controlled experiments. The influence of the pedestrians' behaviours is investigated by prescribing a selfish attitude to a fraction c_s of the participants, while the others behave politely. Thanks to an original setup enabling the re-injection of egressed participants into the room, the analysis is conducted in a (macroscopically) quasi-stationary regime. We find that, as c_s is increased, the flow rate J rises, interpolating between published values for egresses in normal conditions and measurements for competitive evacuations. The dependence of several flow properties on the pedestrian density ρ at the door, independently of c_s , suggests that macroscopically the behavioural aspects could be subsumed under the density, at least in our specific settings with limited crowd pressure. In particular, under these conditions, J grows monotonically with ρ up to " close-packing " (ρ ≈ 9 pers/m²). The flow is then characterised microscopically. Among other quantities, the time lapses between successive escapes, the pedestrians' waiting times in front of the door, and their angles of incidence are analysed statistically. In a nutshell, our main results show that the flow is orderly for polite crowds, with narrowly distributed time lapses between egresses, while for larger c_s the flow gets disorderly and vanishing time lapses emerge. For all c_s , we find an alternation between short and long time lapses, which we ascribe to a generalised zipper effect. The average waiting time in the exit zone increases with its occupancy. The disorder in the flow and the pressure felt by participants are also assessed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centre Atomico Bariloche, CNEA and CONICET
- 3. Instituto Balseiro

## P-wave superfluidity of atomic lattice fermions

### A. K. Fedorov

^{1, 2}V. I. Yudson^{3, 1}G. V. Shlyapnikov^{4, 5, 1, 2, 6}*Physical Review A*, American Physical Society, 2017, 95 (4), pp.043615We discuss the emergence of p-wave superfluidity of identical atomic fermions in a two-dimensional optical lattice. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermion sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, for moderate lattice depths the enhancement of the density of states can compensate the decrease of the scattering amplitude. Moreover, the lattice setup significantly reduces inelastic collisional losses, which allows one to get closer to a p-wave Feshbach resonance. This opens possibilities to obtain the topological $p_x+ip_y$ superfluid phase, especially in the recently proposed subwavelength lattices. We demonstrate this for the two-dimensional version of the Kronig-Penney model allowing a transparent physical analysis.

- 1. Russian Quantum Center
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. National Research University Higher School of Economics [Moscow]
- 4. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 5. Wuhan Institute of Physics and Mathematics
- 6. SPEC - UMR3680 - Service de physique de l'état condensé

## On Thouless bandwidth formula in the Hofstadter model

### Stéphane Ouvry

^{1}Shuang Wu^{1}*Journal of Physics A: Mathematical and General*, IOP Publishing, 2017We generalize Thouless bandwidth formula to its n-th moment. We obtain a closed expression in terms of polygamma, zeta and Euler numbers.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Nonlinear mechanical response of supercooled melts under applied forces

### Heliana Cárdenas

^{1}Fabian Frahsa^{2}Sebastian Fritschi^{2}Alexandre Nicolas^{3}Simon Papenkort^{1}Thomas Voigtmann^{1, 4}Matthias Fuchs^{2}*European Physical Journal - Special Topics*, EDP Sciences, 2017, 226 (14), pp.3039 - 3060. 〈10.1140/epjst/e2017-70079-3〉- 1. Institut für Materialphysik im Weltraum
- 2. Fachbereich Physik [Konstanz]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Institut fur Theoretische Physik

## Non-equilibrium fluctuations of a semi-flexible filament driven by active cross-linkers

### Ines Weber

^{1, 2}Cecile Appert-Rolland^{2}Gregory Schehr^{3}Ludger Santen^{1}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017The cytoskeleton is an inhomogeneous network of semi-flexible filaments, which are involved in a wide variety of active biological processes. Although the cytoskeletal filaments can be very stiff and embedded in a dense and cross-linked network, it has been shown that, in cells, they typically exhibit significant bending on all length scales. In this work we propose a model of a semi-flexible filament deformed by different types of cross-linkers for which one can compute and investigate the bending spectrum. Our model allows to couple the evolution of the deformation of the semi-flexible polymer with the stochastic dynamics of linkers which exert transversal forces onto the filament. We observe a $q^{-2}$ dependence of the bending spectrum for some biologically relevant parameters and in a certain range of wavenumbers $q$. However, generically, the spatially localized forcing and the non-thermal dynamics both introduce deviations from the thermal-like $q^{-2}$ spectrum.

- 1. Saarland University [Saarbrücken]
- 2. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Non-equilibrium Fluctuational Quantum Electrodynamics: Heat Radiation, Heat Transfer, and Force

### G. Bimonte

^{1, 2}T. Emig^{3, 4}M. Kardar^{3}M. Krüger^{5}*Annual Review of Condensed Matter Physics*, 2017, 8, pp.119Quantum and thermal fluctuations of electromagnetic waves are the cornerstone of quantum and statistical physics, and inherent to such phenomena as thermal radiation and van der Waals forces. While the basic principles are the material of elementary texts, recent experimental and technological advances have made it necessary to come to terms with counterintuitive consequences of electromagnetic fluctuations at short scales -- in the so called {\it near-field} regime. We focus on three manifestations of such behavior: {\bf (i)} The Stefan--Boltzmann law describes thermal radiation from macroscopic bodies, but fails to account for magnitude, polarization and coherence of radiation from small objects (say compared to the skin depth). {\bf (ii)} The heat transfer between two bodies at similar close proximity is dominated by evanescent waves, and can be several orders of magnitude larger than the classical contribution due to propagating waves. {\bf (iii)} Casimir/van der Waals interactions are a dominant force between objects at sub-micron separation; the non-equilibrium analogs of this force (for objects at different temperatures) have not been sufficiently explored (at least experimentally). To explore these phenomena we introduce the tool of fluctuational quantum electrodynamics (QED) originally introduced by Rytov in the 1950s. Combined with a scattering formalism, this enables studies of heat radiation and transfer, equilibrium and non-equilibrium forces for objects of different material properties, shapes, separations and arrangements.

- 1. Università degli studi di Napoli Federico II
- 2. INFN, Sezione di Napoli - Istituto Nazionale di Fisica Nucleare, Sezione di Napoli
- 3. MIT - Massachusetts Institute of Technology
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Max Planck Institute for Intelligent Systems

## Modification of the Porter-Thomas distribution by rank-one interaction

### E. Bogomolny

^{1}*Physical Review Letters*, American Physical Society, 2017, 118 (2), pp.022501The Porter-Thomas (PT) distribution of resonance widths is one of the oldest and simplest applications of statistical ideas in nuclear physics. Previous experimental data confirmed it quite well but recent and more careful investigations show clear deviations from this distribution. To explain these discrepancies the authors of [PRL \textbf{115}, 052501 (2015)] argued that to get a realistic model of nuclear resonances is not enough to consider one of the standard random matrix ensembles which leads immediately to the PT distribution but it is necessary to add a rank-one interaction which couples resonances to decay channels. The purpose of the paper is to solve this model analytically and to find explicitly the modifications of the PT distribution due to such interaction. Resulting formulae are simple, in a good agreement with numerics, and could explain experimental results.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Mechanistic understanding toward the toxicity of graphene-family materials to freshwater algae

### J. Zhao

^{1}X. Cao^{2}Z. Wang^{3}Y. Dai^{4}B. Xing*Water Res*, 2017, 111, pp.18-27. 〈10.1016/j.watres.2016.12.037〉no abstract

- 1. Shenzhen University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. BIOVERT - BIOVERT
- 4. LPEM - Laboratoire de Physique et d'Etude des Matériaux

## Mechanisms of jamming in the Nagel-Schreckenberg model for traffic flow

### Henrik Bette

^{1, 2}Lars Habel^{2}Thorsten Emig^{3, 1, 4}Michael Schreckenberg^{2}*Physical Review E*, American Physical Society (APS), 2017, 95 (1), 〈10.1103/PhysRevE.95.012311〉- 1. MSE2 - Multiscale Materials Science for Energy and Environment
- 2. Universität Duisburg-Essen [Essen]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. MIT - Massachusetts Institute of Technology

## Mean-field avalanches in jammed spheres

### Silvio Franz

^{1}Stefano Spigler^{1}*Physical Review E*, American Physical Society (APS), 2017, 95 (2), pp.022139Disordered systems are characterized by the existence of many sample- dependent local energy minima, that cause a stepwise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three dimensional systems of soft-spheres, either at jamming or at slightly higher densities.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Mean perimeter and mean area of the convex hull over planar random walks

### Denis S. Grebenkov

^{1}Yann Lanoiselée^{2}Satya N. Majumdar^{3}Denis Grebenkov^{1}Satya N Majumdar^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017, 2017 (10), 〈10.1088/1742-5468/aa8c11〉We investigate the geometric properties of the convex hull over $n$ successive positions of a planar random walk, with a symmetric continuous jump distribution. We derive the large $n$ asymptotic behavior of the mean perimeter. In addition, we compute the mean area for the particular case of isotropic Gaussian jumps. While the leading terms of these asymptotics are universal, the subleading (correction) terms depend on finer details of the jump distribution and describe a "finite size effect" of discrete-time jump processes, allowing one to accurately compute the mean perimeter and the mean area even for small $n$, as verified by Monte Carlo simulations. This is particularly valuable for applications dealing with discrete-time jumps processes and ranging from the statistical analysis of single-particle tracking experiments in microbiology to home range estimations in ecology.

- 1. LPMC - Laboratoire de physique de la matière condensée
- 2. LPMC - Laboratoire de Physique de la Matière Condensée
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Many body heat radiation and heat transfer in the presence of a non-absorbing background medium

### Muller Boris

^{1}Incardone Roberta^{1}Mauro Antezza^{2, 3}Emig Thorsten^{4, 5}Kruger Matthias^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95, pp.085413. 〈10.1103/PhysRevB.95.085413〉Heat radiation and near-field radiative heat transfer can be strongly manipulated by adjusting geometrical shapes, optical properties, or the relative positions of the objects involved. Typically, these objects are considered as embedded in vacuum. By applying the methods of fluctuational electrodynamics, we derive general closed-form expressions for heat radiation and heat transfer in a system of N arbitrary objects embedded in a passive nonabsorbing background medium. Taking into account the principle of reciprocity, we explicitly prove the symmetry and positivity of transfer in any such system. Regarding applications, we find that the heat radiation of a sphere as well as the heat transfer between two parallel plates is strongly enhanced by the presence of a background medium. Regarding near- and far-field transfer through a gas like air, we show that a microscopic model (based on gas particles) and a macroscopic model (using a dielectric contrast) yield identical results. We also compare the radiative transfer through a medium like air and the energy transfer found from kinetic gas theory.

- 1. Max Planck Institute for Intelligent Systems
- 2. L2C - Laboratoire Charles Coulomb
- 3. Théorie du rayonnement matière et phénomènes quantiques
- 4. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Loop expansion around the Bethe approximation through the $M$-layer construction

### Ada Altieri

^{1, 2}Maria Chiara Angelini^{3}Carlo Lucibello^{4}Giorgio Parisi^{5, 6, 7}Federico Ricci-Tersenghi^{8, 6, 7}Tommaso Rizzo^{9, 10}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017For every physical model defined on a generic graph or factor graph, the Bethe $M$-layer construction allows building a different model for which the Bethe approximation is exact in the large $M$ limit and it coincides with the original model for $M=1$. The $1/M$ perturbative series is then expressed by a diagrammatic loop expansion in terms of so-called fat-diagrams. Our motivation is to study some important second-order phase transitions that do exist on the Bethe lattice but are either qualitatively different or absent in the corresponding fully connected case. In this case the standard approach based on a perturbative expansion around the naive mean field theory (essentially a fully connected model) fails. On physical grounds, we expect that when the construction is applied to a lattice in finite dimension there is a small region of the external parameters close to the Bethe critical point where strong deviations from mean-field behavior will be observed. In this region, the $1/M$ expansion for the corrections diverges and it can be the starting point for determining the correct non-mean-field critical exponents using renormalization group arguments. In the end, we will show that the critical series for the generic observable can be expressed as a sum of Feynman diagrams with the same numerical prefactors of field theories. However, the contribution of a given diagram is not evaluated associating Gaussian propagators to its lines as in field theories: one has to consider the graph as a portion of the original lattice, replacing the internal lines with appropriate one-dimensional chains, and attaching to the internal points the appropriate number of infinite-size Bethe trees to restore the correct local connectivity of the original model.

- 1. Department of Physics [Roma La Sapienza]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Dipartimento di Fisica, Sapienza Università di Roma
- 4. Polito - Politecnico di Torino [Torino]
- 5. Dipartimento di Fisica
- 6. S.Li.M. Lab - Soft and Living Matter Laboratory
- 7. Sapienza Universit'a di Roma and Sezione INFN
- 8. Dipartimento di Fisica and INFM
- 9. Dipartimento di Fisica [Roma La Sapienza]
- 10. ISC - Institute for Complex Systems, CNR-Italy

## Long time scaling behaviour for diffusion with resetting and memory

### Denis Boyer

^{1}Martin R. Evans^{2}Satya N. Majumdar^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017, 2017 (2), pp.023208We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory kernel, we show analytically how different asymptotic behaviours of the variance of the particle position emerge at long times. These range from standard diffusive ($\sigma^2 \sim t$) all the way to anomalous ultraslow growth $\sigma^2 \sim \ln \ln t$.

- 1. UNAM - Universidad Nacional Autónoma de México
- 2. SUPA - School of Physics, University of Edinburgh
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Localization Transition Induced by Learning in Random Searches

### Andrea Falcón-Cortés

^{1}Denis Boyer^{2}Luca Giuggioli^{3}Satya N. Majumdar^{4}*Physical Review Letters*, American Physical Society, 2017, 119 (14), 〈10.1103/PhysRevLett.119.140603〉We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the resetting rate crosses a threshold above which non-diffusive stationary states emerge, localized around the inhomogeneity. The threshold depends on the trapping strength and on the walker's return probability in the memoryless case. The transition belongs to the same class as the self-consistent theory of Anderson localization. These results show that similarly to many living organisms and unlike the well-studied Markovian walks, non-Markov movement processes can allow agents to learn about their environment and promise to bring adaptive solutions in search tasks.

- 1. UNAM - Universidad Nacional Autónoma de México
- 2. Instituto de Fisica
- 3. University of Bristol [Bristol]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Liouville field theory and log-correlated Random Energy Models

### Xiangyu Cao

^{1}Alberto Rosso^{1}Raoul Santachiara^{1}Pierre Le Doussal^{2}Pierre Le Doussal^{2}*Physical Review Letters*, American Physical Society, 2017, 118 (9), pp.090601An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry breaking methods. Operator product expansions in LFT allow to unveil novel universal behaviours of the log-correlated Random Energy class. High precision numerical tests are given.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Large deviations

### Satya N. Majumdar

^{1}Gregory Schehr^{1}*ICTS newsletter*, 2017This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Kinetic energy of a trapped Fermi gas at finite temperature

### Jacek Grela

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Physical Review Letters*, American Physical Society, 2017, 119, pp.130601We study the statistics of the kinetic (or equivalently potential) energy for $N$ non-interacting fermions in a $1d$ harmonic trap of frequency $\omega$, at finite temperature $T$. Remarkably, we find an exact solution for the full distribution of the kinetic energy, at any temperature $T$ and for any $N$, using a non-trivial mapping to an integrable Calogero-Moser-Sutherland model. As a function of temperature $T$, and for large $N$, we identify: (i) a quantum regime, for $T \sim \hbar \omega$, where quantum fluctuations dominate and (ii) a thermal regime, for $T \sim N \hbar \omega$, governed by thermal fluctuations. We show how the mean, the variance as well as the large deviation function associated with the distribution of the kinetic energy cross over from the quantum to the thermal regime as temperature increases.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Geometrical frustration yields fiber formation in self-assembly

### Martin Lenz

^{1}Thomas A. Witten^{2}*Nature Physics*, Nature Publishing Group, 2017Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined morphologies. This is the case in numerous medical conditions where normally soluble proteins aggregate into fibers. Beyond the diversity of molecular mechanisms involved, we propose that fibers generically arise from the aggregation of irregular particles with short-range interactions. Using a minimal model of ill-fitting, sticky particles, we demonstrate robust fiber formation for a variety of particle shapes and aggregation conditions. Geometrical frustration plays a crucial role in this process, and accounts for the range of parameters in which fibers form as well as for their metastable character.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Chicago

## Genuinely entangled symmetric states with no N -partite correlations

### S. Designolle

^{1, 2}O. Giraud^{2}J. Martin^{3}*Physical Review A*, American Physical Society, 2017, 96 (3), pp.032322. 〈10.1103/PhysRevA.96.032322〉We investigate genuinely entangled $N$-qubit states with no $N$-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of $N$-partite correlations. We show that symmetric states with no $N$-partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no $N$-partite correlations in the case of three qubits, and in the case of rank-two states. We present a general procedure to construct families for arbitrary odd number of qubits.

- 1. Ecole Polytechnique - X
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institut de Physique Nucl'eaire, Atomique et de Spectroscopie

## Genuine localisation transition in a long-range hopping model

### Xiangyu Cao

^{1}Alberto Rosso^{1}Jean-Philippe Bouchaud^{2}Pierre Le Doussal^{3}*Physical Review E*, American Physical Society (APS), 2017, 95 (6), pp.062118We introduce and study a new class of Banded Random Matrix model describing sparse, long range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and mappings to statistical physics models, we establish the phase diagram of the model. A genuine localisation transition, with well defined mobility edges, appears as the hopping rate decreases slower than $\ell^{-2}$, where $\ell$ is the distance. Correspondingly, the decay of the localised states evolves from a standard exponential shape to a stretched exponential and finally to a novel $\exp(-C\ln^\kappa \ell)$ behaviour, with $\kappa > 1$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CFM - Capital Fund Management
- 3. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Fulde-Ferrell-Larkin-Ovchinnikov state in bilayer dipolar systems

### Hao Lee

^{1, 2, 3}S. I. Matveenko^{3, 4}Daw-Wei Wang^{1, 2}G. V. Shlyapnikov^{3, 5, 6, 7, 8}*Physical Review A*, American Physical Society, 2017, 96 (6), 〈10.1103/PhysRevA.96.061602〉We study the phase diagram of fermionic polar molecules in a bilayer system, with an imbalance of molecular densities of the layers. For the imbalance exceeding a critical value the system undergoes a transition from the uniform interlayer superfluid to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with a stripe structure, and at sufficiently large imbalance a transition from the FFLO to normal phase. Compared to the case of contact interactions, the FFLO regime is enhanced by the long-range character of the interlayer dipolar interaction, which can combine the s-wave and p-wave pairing in the order parameter.

- 1. NTHU - National Tsing Hua University [Hsinchu]
- 2. NCTS - National Center for Theoretical Sciences [Taiwan]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. L.D. Landau Institute for Theoretical Physics of RAS
- 5. SPEC - UMR3680 - Service de physique de l'état condensé
- 6. Russian Quantum Center
- 7. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 8. Wuhan Institute of Physics and Mathematics

## Fragmented-condensate solid of dipolar excitons

### S. V. Andreev

^{1, 2, 3}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95 (18), pp.184519. 〈10.1103/PhysRevB.95.184519〉We discuss a possible link between the recently observed macroscopic ordering of ultracold dipolar excitons (MOES) and the phenomenon of supersolidity. In the dilute limit we predict a stable supersolid state for a quasi-one-dimensional system of bosonic dipoles characterized by two-and three-body contact repulsion. We phenomenologically extend our theory to the strongly-correlated regime and find a critical value of the contact interaction parameter at which the supersolid exhibits a quantum phase transition to a fragmented state. The wavelength of the fragmented-condensate solid is defined by the balance between the quantum pressure and the entropy due to fluctuations of the relative phases between the fragments. Our model appears to be in good agreement with the relevant experimental data, including the very recent results on commensurability effect and wavelength of the MOES.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. ITMO - National Research University of Information Technologies, Mechanics and Optics [St. Petersburg]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions

### Kirill Plekhanov

^{1, 2}Guillaume Roux^{2}Karyn Le Hur^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95, pp.045102The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically non-trivial band structure associated with chiral edge modes (without the presence of a net unit flux in a unit cell), then referring to the quantum anomalous Hall effect. Focusing on (interacting) boson systems in s-wave bands of the lattice, we show how to engineer through the Floquet theory, a quantum phase transition between a uniform superfluid and a BEC (Bose-Einstein Condensate) analog of FFLO (Fulde-Ferrell-Larkin-Ovchinnikov) states, where bosons condense at non-zero wave-vectors. We perform a Ginzburg-Landau analysis of the quantum phase transition on the graphene lattice, and compute observables such as chiral currents and the momentum distribution. The results are supported by exact diagonalization calculations and compared with those of the isotropic situation. The validity of high-frequency expansion in the Floquet theory is also tested using time-dependent simulations for various parameters of the model. Last, we show that the anisotropic choice for the effective vector potential allows a bosonization approach in equivalent ladder (strip) geometries.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures

### Betzalel Bazak

^{1}Dmitry S. Petrov^{2, 3}*Physical Review Letters*, American Physical Society, 2017, 118 (8), pp.083002We show that four heavy fermions interacting resonantly with a lighter atom (4+1 system) become Efimovian at mass ratio 13.279(2), which is smaller than the corresponding 2+1 and 3+1 thresholds. We thus predict the five-body Efimov effect for this system in the regime where any of its subsystem is non- Efimovian. For smaller mass ratios we show the existence and calculate the energy of a universal 4+1 pentamer state, which continues the series of the 2+1 trimer predicted by Kartavtsev and Malykh and 3+1 tetramer discovered by Blume. We also show that the effective-range correction for the light-heavy interaction has a strong effect on all these states and larger effective ranges increase their tendency to bind.

- 1. IPNO - Institut de Physique Nucléaire d'Orsay
- 2. Kavli Institute for Theoretical Institute
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## First Gap Statistics of Long Random Walks with Bounded Jumps

### Philippe Mounaix

^{1}Gregory Schehr^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2017, 50 (18), pp.185001We study one-dimensional discrete as well as continuous time random walks, either with a fixed number of steps (for discrete time) $n$ or on a fixed time interval $T$ (for continuous time). In both cases, we focus on symmetric probability distribution functions (PDF) of jumps with a finite support $[-g_{max}, g_{max}]$. For continuous time random walks (CTRWs), the waiting time $\tau$ between two consecutive jumps is a random variable whose probability distribution (PDF) has a power law tail $\Psi(\tau) \propto \tau^{-1-\gamma}$, with $0<\gamma<1$. We obtain exact results for the joint statistics of the gap between the first two maximal positions of the random walk and the time elapsed between them. We show that for large $n$ (or large time $T$ for CTRW), this joint PDF reaches a stationary joint distribution which exhibits an interesting concentration effect in the sense that a gap close to its maximum possible value, $g\approx g_{max}$, is much more likely to be achieved by two successive jumps rather than by a long walk between the first two maxima. Our numerical simulations confirm this concentration effect.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Extensile actomyosin?

### Martin Lenz

^{1}*European Biophysics Journal with Biophysics Letters*, 2017Living cells move thanks to assemblies of actin filaments and myosin motors that range from very organized striated muscle tissue to disordered intracellular bundles. The mechanisms powering these disordered structures are debated, and all models studied so far predict that they are contractile. We reexamine this prediction through a theoretical treatment of the interplay of three well-characterized internal dynamical processes in actomyosin bundles: actin treadmilling, the attachement-detachment dynamics of myosin and that of crosslinking proteins. We show that these processes enable an extensive control of the bundle's active mechanics, including reversals of the filaments' apparent velocities and the possibility of generating extension instead of contraction. These effects offer a new perspective on well-studied in vivo systems, as well as a robust criterion to experimentally elucidate the underpinnings of actomyosin activity.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Exact Extremal Statistics in the Classical 1D Coulomb Gas

### Abhishek DharAnupam KunduSatya Majumdar

^{1}Sanjib SabhapanditGrégory Schehr^{1}*Phys.Rev.Lett.*, 2017, 119 (6), pp.060601. 〈10.1103/PhysRevLett.119.060601〉We consider a one-dimensional classical Coulomb gas of N-like charges in a harmonic potential—also known as the one-dimensional one-component plasma. We compute, analytically, the probability distribution of the position xmax of the rightmost charge in the limit of large N. We show that the typical fluctuations of xmax around its mean are described by a nontrivial scaling function, with asymmetric tails. This distribution is different from the Tracy-Widom distribution of xmax for Dyson’s log gas. We also compute the large deviation functions of xmax explicitly and show that the system exhibits a third-order phase transition, as in the log gas. Our theoretical predictions are verified numerically.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

### T. Congy

^{1}S. K. Ivanov^{2, 3}A. M. Kamchatnov^{4}N. Pavloff^{1}*Chaos*, American Institute of Physics, 2017, 27 (8), pp.083107. 〈10.1063/1.4997052〉We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. MIPT - Moscow Institute of Physics and Technology [Moscow]
- 3. Institute of Spectroscopy
- 4. Institute of Spectroscopy

## Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade

### Yong Zeng

^{1}Peng Xu^{1}Xiaodong He^{1}Yangyang Liu^{1}Min Liu^{1}Jin Wang^{1}D. j. Papoular^{2}G. v. Shlyapnikov^{3}Mingsheng Zhan^{1}*Physical Review Letters*, American Physical Society, 2017, 119 (16), 〈10.1103/PhysRevLett.119.160502〉Quantum entanglement is crucial for simulating and understanding exotic physics of strongly correlated many-body systems, such as high--temperature superconductors, or fractional quantum Hall states. The entanglement of non-identical particles exhibits richer physics of strong many-body correlations and offers more opportunities for quantum computation, especially with neutral atoms where in contrast to ions the interparticle interaction is widely tunable by Feshbach resonances. Moreover, the inter-species entanglement forms a basis for the properties of various compound systems, ranging from Bose-Bose mixtures to photosynthetic light-harvesting complexes. So far, the inter-species entanglement has only been obtained for trapped ions. Here we report on the experimental realization of entanglement of two neutral atoms of different isotopes. A ${}^{87}\mathrm{Rb}$ atom and a ${}^{85}\mathrm{Rb}$ atom are confined in two single--atom optical traps separated by 3.8 $\mu$m. Creating a strong Rydberg blockade, we demonstrate a heteronuclear controlled--NOT (C--NOT) quantum gate and generate a heteronuclear entangled state, with raw fidelities $0.73 \pm 0.01$ and $0.59 \pm 0.03$, respectively. Our work, together with the technologies of single--qubit gate and C--NOT gate developed for identical atoms, can be used for simulating any many--body system with multi-species interactions. It also has applications in quantum computing and quantum metrology, since heteronuclear systems exhibit advantages in low crosstalk and in memory protection.

- 1. State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071 China
- 2. LPTM - Laboratoire de Physique Théorique et Modélisation
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Entanglement and the truncated moment problem

### Fabian Bohnet-Waldraff

^{1, 2}Daniel Braun^{2}Olivier Giraud^{1}*Physical Review A*, American Physical Society, 2017, 96 (3), pp.032312. 〈10.1103/PhysRevA.96.032312〉We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semi-definite programs. The algorithm always gives a certificate of entanglement if the state is entangled. If the state is separable, typically a certificate of separability is obtained in a finite number of steps and an explicit decomposition into separable pure states can be extracted.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institut für Physikalische und Theoretische Chemie

## Enhanced Dynamics of Confined Cytoskeletal Filaments Driven by Asymmetric Motors

### Arvind Ravichandran

^{1}Gerrit A. Vliegenthart^{1}Guglielmo Saggiorato^{1, 2}Thorsten Auth^{1}Gerhard Gompper^{1}*Biophysical Journal*, Biophysical Society, 2017, 113 (5), pp.1121 - 1132. 〈10.1016/j.bpj.2017.07.016〉- 1. Institute of Complex Systems and Institute for Advanced Simulation
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Distinguishing humans from computers in the game of go: A complex network approach

### C. Coquidé

^{1}Bertrand Georgeot^{1}Olivier Giraud^{2}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017, 119 (4), pp.48001. 〈10.1209/0295-5075/119/48001〉We compare complex networks built from the game of go and obtained from databases of human-played games with those obtained from computer-played games. Our investigations show that statistical features of the human-based networks and the computer-based networks differ, and that these differences can be statistically significant on a relatively small number of games using specific estimators. We show that the deterministic or stochastic nature of the computer algorithm playing the game can also be distinguished from these quantities. This can be seen as tool to implement a Turing-like test for go simulators.

- 1. Information et Chaos Quantiques (LPT)
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Convex hulls of random walks in higher dimensions: A large-deviation study

### Hendrik Schawe

^{1}Alexander K. Hartmann^{1}Satya N. Majumdar^{2}*Physical Review E*, American Physical Society (APS), 2017, 96 (6), 〈10.1103/PhysRevE.96.062101〉The distribution of the hypervolume $V$ and surface $\partial V$ of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than $P = 10^{-1000}$ to estimate large deviation properties. For arbitrary dimensions and large walk lengths $T$, we suggest a scaling behavior of the distribution with the length of the walk $T$ similar to the two-dimensional case, and behavior of the distributions in the tails. We underpin both with numerical data in $d=3$ and $d=4$ dimensions. Further, we confirm the analytically known means of those distributions and calculate their variances for large $T$.

- 1. University of Oldenburg
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions

### Jerome Dubail

^{1}Raoul Santachiara^{2}Thorsten Emig^{3, 2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017, pp.033201Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szeg\"o formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface Renormalization Group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.

- 1. Equipe 106, IJL - Groupe de Physique statistique = Statistical Physics Group [Institut Jean Lamour]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MIT - Massachusetts Institute of Technology

## Configurational and energy landscape in one-dimensional Coulomb systems

### Lucas Varela

^{1}Gabriel Téllez^{1}Emmanuel Trizac^{2}*Physical Review E*, American Physical Society (APS), 2017, 95 (2), pp.022112We study a one dimensional Coulomb system, where two charged colloids are neutralized by a collection of point counterions, with global neutrality. Temperature being given, two situations are addressed: the colloids are either kept at fixed positions (canonical ensemble), or the force acting on the colloids is fixed (isobaric-isothermal ensemble). The corresponding partition functions are worked out exactly, in view of determining which arrangement of counterions is optimal: how many counterions should be in the confined segment between the colloids? For the remaining ions outside, is there a left/right symmetry breakdown? We evidence a cascade of transitions, as system size is varied in the canonical treatment, or as pressure is increased in the isobaric formulation.

- 1. Universidad de los Andes
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Conditioned random walks and interaction-driven condensation

### Juraj Szavits-Nossan

^{1}Martin R. Evans^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2017, 50 (2), pp.024005We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having area $a$ and returning to the origin for the first time after time $\tau$. We then show how condensation occurs when the total area constraint is increased: an excursion containing a finite fraction of the area emerges. Finally we show how the phenomena generalises previously studied cases of condensation induced by several constraints and how it is related to interaction-driven condensation which allows us to explain the phenomenon in the framework of large deviation theory.

- 1. SUPA, School of Physics, University of Edinburgh
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Cleaning large correlation matrices: tools from random matrix theory

### Joël Bun

^{1, 2}Jean-Philippe Bouchaud^{2}Marc Potters^{2}*Physics Reports*, Elsevier, 2017, 666, pp.1This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CFM - Capital Fund Management

## Bloch oscillations in the absence of a lattice

### Florian Meinert

^{1}Michael Knap^{2}Emil Kirilov^{1}Katharina Jag-Lauber^{1}Mikhail B. Zvonarev^{3}Eugene Demler^{4}Hanns-Christoph Nägerl^{1}*Science*, American Association for the Advancement of Science, 2017, 356 (6341), pp.945 - 948We experimentally investigate the quantum motion of an impurity atom that is immersed in a strongly interacting one-dimensional Bose liquid and is subject to an external force. We find that the momentum distribution of the impurity exhibits characteristic Bragg reflections at the edge of an emergent Brillouin zone. While Bragg reflections are typically associated with lattice structures, in our strongly correlated quantum liquid they result from the interplay of short-range crystalline order and kinematic constraints on the many-body scattering processes in the one-dimensional system. As a consequence, the impurity exhibits periodic dynamics that we interpret as Bloch oscillations, which arise even though the quantum liquid is translationally invariant. Our observations are supported by large-scale numerical simulations.

- 1. Institut für Experimentalphysik und Zentrum für Quantenphysik Universitat Innsbruck
- 2. TUM - Technical University of Munich
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Harvard University [Cambridge]

## Avalanches dynamics in reaction fronts in disordered flows

### T. Chevalier

^{1}A. Dubey^{1}S. Atis^{1}A. Rosso^{2}D. Salin^{1}L. Talon^{1}*Physical Review E*, American Physical Society (APS), 2017, 95 (4), 〈10.1103/PhysRevE.95.042210〉- 1. FAST - Fluides, automatique, systèmes thermiques
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Asymptotically optimal control for a simplest distributed system

### Alexander Ovseevich

^{1}Aleksey Fedorov^{2}*Доклады Академии Наук / Doklady Mathematics*, MAIK Nauka/Interperiodica, 2017, 95 (2), pp.194 - 197We study the problem of the minimum-time damping of a closed string under a bounded load, applied at a single fixed point. A constructive feedback control law is designed, which allows bringing the system to a bounded neighbourhood of the terminal manifold. The law has the form of the dry friction at the point, where the load is applied. The motion under the control is governed by a nonlinear wave equation. The existence and uniqueness of solution of the Cauchy problem for this equation are proved. The main result is the asymptotic optimality of the suggested control law.

- 1. Institute for Problems in Mechanics of Russian Academy of Sciences
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Statistics of fermions in a d-dimensional box near a hard wall

### Bertrand Lacroix-A-Chez-Toine

^{1}Pierre Le Doussal^{2}Satya Majumdar^{1}Grégory Schehr^{1}*EPL*, 2017, 120 (1), pp.10006. 〈10.1209/0295-5075/120/10006〉We study N noninteracting fermions in a domain bounded by a hard-wall potential in dimensions. We show that for large N, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth confining potentials. We compute this d-dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any sufficiently smooth boundary. As an application we compute the quantum statistics of the position of the fermion closest to the hard wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Statistics of fermions in a $d$-dimensional box near a hard wall

### Bertrand Lacroix-A-Chez-Toine

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Gregory Schehr^{1}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017We study $N$ noninteracting fermions in a domain bounded by a hard wall potential in $d \geq 1$ dimensions. We show that for large $N$, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth potentials. We compute this $d$ dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any sufficiently smooth boundary. As an application we compute the quantum statistics of the position of the fermion closest to the wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Quantum quenches with random matrix Hamiltonians and disordered potentials

### Fabian Kolley

^{1}Oriol Bohigas^{2}Boris V. Fine^{1, 3}*Annalen der Physik*, 2017We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists of sudden switching-on the off-diagonal elements of the Hamiltonian. In the latter case, it is sudden switching-on of the hopping between adjacent lattice sites. The quench-induced ensembles are compared with the so-called "quantum micro-canonical" (QMC) ensemble describing quantum superpositions with fixed energy expectation values. Our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the QMC ensemble. Away from the QMC condensation regime, the overall agreement with the QMC predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate.

- 1. University of Heidelberg
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Skoltech - Skolkovo Institute of Science and Technology [Moscow]

## Archive ouverte HAL – Non-equilibrium fluctuations of a semi-flexible filament driven by active cross-linkers

### Ines Weber

^{1, 2}Cecile Appert-Rolland^{2}Gregory Schehr^{3}Ludger Santen^{1}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017The cytoskeleton is an inhomogeneous network of semi-flexible filaments, which are involved in a wide variety of active biological processes. Although the cytoskeletal filaments can be very stiff and embedded in a dense and cross-linked network, it has been shown that, in cells, they typically exhibit significant bending on all length scales. In this work we propose a model of a semi-flexible filament deformed by different types of cross-linkers for which one can compute and investigate the bending spectrum. Our model allows to couple the evolution of the deformation of the semi-flexible polymer with the stochastic dynamics of linkers which exert transversal forces onto the filament. We observe a $q^{-2}$ dependence of the bending spectrum for some biologically relevant parameters and in a certain range of wavenumbers $q$. However, generically, the spatially localized forcing and the non-thermal dynamics both introduce deviations from the thermal-like $q^{-2}$ spectrum.

- 1. Saarland University [Saarbrücken]
- 2. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Large deviations

### Satya N. Majumdar

^{1}Gregory Schehr^{1}*ICTS newsletter*, 2017This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Hall voltage drives pulsing counter-currents of the sliding charge density wave and of quantized normal carriers at self-filled Landau levels

### Andrey Orlov

^{1}Aleksander Sinchenko^{1}Pierre Monceau^{2}Serguei Brazovskii^{3}Yuri Latyshev^{1}*npj Quantum Materials*, 2017, 2 (1), pp.61. 〈10.1038/s41535-017-0070-3〉- 1. IRE - Kotel'nikov Institute of Radio Engineering and Electronics
- 2. MagSup - Magnétisme et Supraconductivité
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade

### Yong Zeng

^{1}Peng Xu^{1}Xiaodong He^{1}Yangyang LiuMin Liu^{2}Jin Wang^{3}D. j. Papoular^{4}G. v. Shlyapnikov^{5}Mingsheng Zhan^{1}#### Yong Zeng, Peng Xu, Xiaodong He, Yangyang Liu, Min Liu, et al.. Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade.

*Physical Review Letters*, American Physical Society, 2017, 119 (16), ⟨10.1103/PhysRevLett.119.160502⟩. ⟨hal-02364114⟩- 1. Wuhan Institute of Physics and Mathematics
- 2. SDAU - Shandong Agricultural University
- 3. Shanghai Institute of Hematology
- 4. LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Ecological plant epigenetics: Evidence from model and non-model species, and the way forward

### Christina RichardsConchita AlonsoClaude Becker

^{1}Oliver Bossdorf^{2}Etienne Bucher^{3}Maria Colome-Tatche^{4}Walter Durka^{5}Jan EngelhardtBence GasparAndreas Gogol-DöringIvo Grosse^{6}Thomas Van GurpKatrin Heer^{7}Ilkka Kronholm^{8}Christian LampeiVít LatzelMarie Mirouze^{9}Lars OpgenoorthOvidiu Paun^{10}Sonja ProhaskaStefan RensingPeter Stadler^{11}Emiliano Trucchi^{12}Kristian UllrichKoen VerhoevenTim Coulson^{13}*Ecology Letters*, Wiley, 2017, 20 (12), pp.1576-1590. 〈10.1111/ele.12858〉- 1. GMI - Gregor Mendel Institute of Molecular Plant Biology
- 2. Plant Evolutionary Ecology
- 3. IRHS - Institut de Recherche en Horticulture et Semences
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. UFZ - Helmholtz Zentrum für Umweltforschung
- 6. Inst Comp Sci
- 7. Institute of Experimental Ecology Germany, Conservation Biology and Ecology
- 8. Department of Plant Breeding and Genetics
- 9. UMR DIADE - Diversité, adaptation, développement des plantes
- 10. Department of Botany and Biodiversity Research
- 11. Carl Maria von Weber—Collected Works
- 12. CEES - Centre for Ecological and Evolutionary Synthesis
- 13. Department of Zoology [Oxford]

## Archive ouverte HAL – Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions

### Jerome Dubail

^{1}R. Santachiara^{2}T. Emig^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017, 2017 (3), pp.033201- 1. LPCT - Laboratoire de Physique et Chimie Théoriques
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MIT - Massachusetts Institute of Technology

## Archive ouverte HAL – Characterizing Thermal Mixing Dynamic Nuclear Polarization via Cross-Talk between Spin Reservoirs

### David Guarin

^{1}Sina Marhabaie^{1}Alberto Rosso^{1, 2}Daniel Abergel^{1}Geoffrey Bodenhausen^{1}Konstantin Ivanov^{3}Dennis Kurzbach^{1}*Journal of Physical Chemistry Letters*, American Chemical Society, 2017, 8 (22), pp.5531-5536. 〈10.1021/acs.jpclett.7b02233〉Dynamic nuclear polarization (DNP) embraces a family of methods to increase signal intensities in nuclear magnetic resonance (NMR) spectroscopy. Despite extensive theoretical work that allows one to distinguish at least five distinct mechanisms, it remains challenging to determine the relative weights of the processes that are responsible for DNP in state-of-the-art experiments operating with stable organic radicals like nitroxides at high magnetic fields and low temperatures. Specifically, determining experimental conditions where DNP involves thermal mixing, which denotes a spontaneous heat exchange between different spin reservoirs, remains challenging. We propose an experimental approach to ascertain the prevalence of the thermal mixing regime by monitoring characteristic signature properties of the time evolution of the hyperpolarization. We find that thermal mixing is the dominant DNP mechanism at high nitroxide radical concentrations, while a mixture of different mechanisms prevails at lower concentrations.

- 1. LBM UMR 7203 - Laboratoire des biomolécules
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. NSU - Novosibirsk State University

## Analysis of coherent quantum cryptography protocol vulnerability to an active beam-splitting attack

### A K KronbergE. O. Kiktenko

^{1}A. K. Fedorov^{2}Y. V. Kurochkin^{3}D. A. Kronberg*Quantum Electronics*, Turpion, 2017, 47 (2), pp.163 - 168We consider a new type of attack on a coherent quantum key distribution protocol [coherent one-way (COW) protocol]. The main idea of the attack consists in measuring individually the intercepted states and sending the rest of them unchanged. We have calculated the optimum values of the attack parameters for an arbitrary length of a channel length and compared this novel attack with a standard beam-splitting attack.

- 1. Bauman Moscow State Technical University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Russian Quantum Center

## Adaptive Response of Actin Bundles under Mechanical Stress

### Florian Rückerl

^{1}Martin Lenz^{2}Timo Betz^{1}John Manzi^{1}Jean-Louis Martiel^{3}Mahassine Safouane^{1}Rajaa Paterski-Boujemaa^{3}Laurent Blanchoin^{3}Cécile Sykes^{1}*Biophysical Journal*, Biophysical Society, 2017, 113 (5), pp.1072 - 1079. 〈10.1016/j.bpj.2017.07.017〉Actin is one of the main components of the architecture of cells. Actin filaments form different polymer networks with versatile mechanical properties that depend on their spatial organization and the presence of cross-linkers. Here, we investigate the mechanical properties of actin bundles in the absence of cross-linkers. Bundles are polymerized from the surface of mDia1-coated latex beads, and deformed by manipulating both ends through attached beads held by optical tweezers, allowing us to record the applied force. Bundle properties are strikingly different from the ones of a homogeneous isotropic beam. Successive compression and extension leads to a decrease in the buckling force that we attribute to the bundle remaining slightly curved after the first deformation. Furthermore, we find that the bundle is solid, and stiff to bending, along the long axis, whereas it has a liquid and viscous behavior in the transverse direction. Interpretation of the force curves using a Maxwell visco-elastic model allows us to extract the bundle mechanical parameters and confirms that the bundle is composed of weakly coupled filaments. At short times, the bundle behaves as an elastic material, whereas at long times, filaments flow in the longitudinal direction, leading to bundle restructuring. Deviations from the model reveal a complex adaptive rheological behavior of bundles. Indeed, when allowed to anneal between phases of compression and extension, the bundle reinforces. Moreover, we find that the characteristic visco-elastic time is inversely proportional to the compression speed. Actin bundles are therefore not simple force transmitters, but instead, complex mechano-transducers that adjust their mechanics to external stimulation. In cells, where actin bundles are mechanical sensors, this property could contribute to their adaptability.

- 1. PCC - Physico-Chimie-Curie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LPCV - Laboratoire de physiologie cellulaire végétale

## Absolutely classical spin states

### F. Bohnet-Waldraff

^{1, 2}O. Giraud^{1}D. Braun^{2}*Physical Review A*, American Physical Society, 2017, 95 (1), pp.012318We introduce the concept of "absolutely classical" spin states, in analogy to absolutely separable states of bi-partite quantum systems. Absolutely classical states are states that remain classical under any unitary transformation applied to them. We investigate the maximum ball of absolutely classical states centered on the fully mixed state that can be inscribed into the set of classical states, and derive a lower bound for its radius as function of the total spin quantum number. The result is compared to the case of absolutely separable states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Eberhard Karls Universität Tübingen

## Wigner time delay and related concepts: Application to transport in coherent conductors

### Christophe Texier

^{1}*Physica E: Low-dimensional Systems and Nanostructures*, Elsevier, 2016, 82, pp.16 - 33- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Velocity Statistics of the Nagel-Schreckenberg Model

### Nicolas Bain

^{1}Thorsten Emig^{1, 2}Franz-Joseph Ulm^{3}Michael Schreckenberg^{4}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.022305The statistics of velocities in the cellular automaton model of Nagel and Schreckenberg for traffic are studied. From numerical simulations, we obtain the probability distribution function (PDF) for vehicle velocities and the velocity-velocity (vv) correlation function. We identify the probability to find a standing vehicle as a potential order parameter that signals nicely the transition between free congested flow for sufficiently large number of velocity states. Our results for the vv correlation function resemble features of a second order phase transition. We develop a 3-body approximation that allows us to relate the PDFs for velocities and headways. Using this relation, an approximation to the velocity PDF is obtained from the headway PDF observed in simulations. We find a remarkable agreement between this approximation and the velocity PDF obtained from simulations.

- 1. Massachussetts Institute of Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Department of Civil and Environmental Engineering
- 4. Universität Duisburg-Essen [Essen]

## Universal three-body recombination and Efimov resonances in an ultracold Li-Cs mixture

### J. Ulmanis

^{1}S. Häfner^{1}R. Pires^{1}F. Werner^{2}D. S. Petrov^{3}E. D. Kuhnle^{1}M. Weidemüller^{4, 1}*Physical Review A*, American Physical Society, 2016, 93, pp.022707We study Efimov resonances via three-body loss in an ultracold two-component gas of fermionic $^6$Li and bosonic $^{133}$Cs atoms close to a Feshbach resonance at 843~G, extending results reported previously [Pires \textit{et al.}, Phys. Rev. Lett. 112, 250404 (2014)] to temperatures around 120~nK. The experimental scheme for reaching lower temperatures is based upon compensating the gravity-induced spatial separation of the mass-imbalanced gases with bichromatic optical dipole traps. We observe the first and second excited Li-Cs-Cs Efimov resonance in the magnetic field dependence of the three-body event rate constant, in good agreement with the universal zero-range theory at finite temperature [Petrov and Werner, Phys. Rev. A 92, 022704 (2015)]. Deviations are found for the Efimov ground state, and the inelasticity parameter $\eta$ is found to be significantly larger than those for single-species systems.

- 1. Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg
- 2. LKB [Collège de France] - Laboratoire Kastler Brossel
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Hefei National Laboratory for Physical Sciences at the Microscale

## Ultradilute Low-Dimensional Liquids

### D. s. Petrov

^{1}G. e. Astrakharchik^{2}*Physical Review Letters*, American Physical Society, 2016, 117 (10), pp.100401- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departament de Fisica i Enginyeria Nuclear, Campus Nord B4-B5

## Tracer diffusion coefficients in a sheared inelastic Maxwell gas

### Vicente Garzó

^{1}Emmanuel Trizac^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, pp.073206We study the transport properties of an impurity in a sheared granular gas, in the framework of the Boltzmann equation for inelastic Maxwell models. We investigate here the impact of a nonequilibrium phase transition found in such systems, where the tracer species carries a finite fraction of the total kinetic energy (ordered phase). To this end, the diffusion coefficients are first obtained for a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. In this situation, the set of coupled Boltzmann equations are solved by means of a Chapman-Enskog-like expansion around the (local) shear flow distributions for each species, thereby retaining all the hydrodynamic orders in the shear rate $a$. Due to the anisotropy induced by the shear flow, three tensorial quantities $D_{ij}$, $D_{p,ij}$, and $D_{T,ij}$ are required to describe the mass transport process instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled algebraic equations, which can be \emph{exactly} solved as functions of the shear rate $a$, the coefficients of restitution $\alpha_{sr}$ and the parameters of the mixture (masses and composition). Once the forms of $D_{ij}$, $D_{p,ij}$, and $D_{T,ij}$ are obtained for arbitrary mole fraction $x_1=n_1/(n_1+n_2)$ (where $n_r$ is the number density of species $r$), the tracer limit ($x_1\to 0$) is carefully considered for the above three diffusion tensors. Explicit forms for these coefficients are derived showing that their shear rate dependence is significantly affected by the order-disorder transition.

- 1. Departamento de Fisica
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model

### Aur Grabsch

^{1, 2}Christophe Texier^{2}*Europhys.Lett.*, 2016, 〈10.1209/0295-5075/116/17004〉We establish the connection between a multichannel disordered model —the 1D Dirac equation with $N\times N$ matrix random mass— and a random matrix model corresponding to a deformation of the Laguerre ensemble. This allows us to derive exact determinantal representations for the density of states and identify its low-energy $(\varepsilon\to0)$ behaviour $\rho(\varepsilon)\sim|\varepsilon|^{\alpha-1}$ . The vanishing of the exponent α for N specific values of the averaged mass over disorder ratio corresponds to N phase transitions of topological nature characterised by the change of a quantum number (Witten index) which is deduced straightforwardly in the matrix model.

- 1. ENS Cachan - École normale supérieure - Cachan
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Time and temperature-dependent correlation function of an impurity in a one-dimensional Fermi gas as a Fredholm determinant

### O. Gamayun

^{1}Andrei G. Pronko^{2}Mikhail B. Zvonarev^{3, 4}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2016, 18, pp.045005We investigate a free one-dimensional spinless Fermi gas, and the Tonks-Girardeau gas interacting with a single impurity particle of equal mass. We obtain a Fredholm determinant representation for the time-dependent correlation function of the impurity particle. This representation is valid for an arbitrary temperature and an arbitrary repulsive or attractive impurity-gas $\delta$-function interaction potential. It includes, as particular cases, the representations obtained for zero temperature and arbitrary repulsion in [Nucl. Phys. B 892, 83 (2015)], and for arbitrary temperature and infinite repulsion in [Nucl. Phys. B 520, 594 (1998)].

- 1. INSTITUUT LORENTZ - Instituut Lorentz
- 2. Steklov Institute of Mathematics at St. Petersburg
- 3. ITMO - National Research University of Information Technologies, Mechanics and Optics [St. Petersburg]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Thermalization and many-body localization in systems under dynamic nuclear polarization

### Andrea De Luca

^{1}Inés Rodríguez-Arias^{1}Markus Müller^{2, 3, 4}Alberto Rosso^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (1), pp.014203- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Paul Scherrer Institute
- 3. The Abdus Salam International Centre for Theoretical Physics
- 4. Unibas - University of Basel

## The simplest model of jamming

### Silvio Franz

^{1}Giorgio Parisi^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.145001We study a well known machine learning model -the perceptron- as a simple model of jamming of hard objects. We exhibit two regimes: 1) a convex optimisation regime where jamming is hypostatic and non-critical. 2) a non convex optimisation regime where jamming is isostatic and critical. We characterise the critical jamming phase through exponents describing the distributions law of forces and gaps. Surprisingly we find that these exponents coincide with the corresponding ones recently computed in high dimensional hard spheres. In addition, modifying the perceptron to a random linear programming problem, we show that isostaticity is not a sufficient condition for singular force and gap distributions. For that, fragmentation of the space of solutions (replica symmetry breaking) appears to be a crucial ingredient. We hypothesise universality for a large class of non-convex constrained satisfaction problems with continuous variables.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica and INFM

## The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential

### Ada Altieri

^{1, 2}Silvio Franz^{2}Giorgio Parisi^{3, 1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, 2016 (9), pp.093301- 1. SMC/INFM - Department of Physics, Sapienza University of Rome
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]

## The free energy of a liquid when viewed as a population of overlapping clusters

### Pierre Ronceray

^{1}Peter Harrowell^{2}*Molecular Simulation*, Taylor & Francis, 2016, 42, pp.1149The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural fluctuations arises from the local athermal constraints imposed by the overlap of adjacent coordination shells. In the context of the recently developed Favoured Local Structure model [Soft Matt. 11, 3322 (2015)], we derive explicit expressions for the structural energy and entropy in the high temperature limit, compare this approximation with simulation data and consider the extension of this free energy to the case of spatial inhomogeneity in the distribution of local structures.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Faculty of Sciences

## The excitonic insulator route through a dynamical phase transition induced by an optical pulse

### Serguei Brazovskii

^{1}Natasha Kirova^{2}We consider a dynamical phase transition induced by a short optical pulse in a system prone to thermodynamical instability. We address the case of pumping to excitons whose density contributes directly to the order parameter. To describe both thermodynamic and dynamic effects on equal footing, we adopt a view of the excitonic insulator for the phase transition and suggest a formation of the Bose condensate for the pumped excitons. The work is motivated by experiments in donor-acceptor organic compounds with a neutral-ionic phase transition coupled to the spontaneous lattice dimerization and to charge transfer excitons. The double nature of the ensemble of excitons leads to an intricate time evolution, in particular to macroscopic quantum oscillations from the interference between the Bose condensate of excitons and the ground state of the excitonic insulator. The coupling of excitons and the order parameter also leads to self-trapping of their wave function, akin to self-focusing in optics. The locally enhanced density of excitons can surpass a critical value to trigger the phase transformation, even if the mean density is below the required threshold. The system is stratified in domains that evolve through dynamical phase transitions and sequences of merging.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## The dynamics of filament assembly define cytoskeletal network morphology

### Giulia Foffano

^{1}Nicolas Levernier^{2}Martin Lenz^{1}*Nature Communications*, Nature Publishing Group, 2016, 7, pp.13827The actin cytoskeleton is a key component in the machinery of eukaryotic cells, and it selfassembles out of equilibrium into a wide variety of biologically crucial structures. While the molecular mechanisms involved are well characterized, the physical principles governing the spatial arrangement of actin filaments are not understood. Here we propose that the dynamics of actin network assembly from growing filaments results from a competition between diffusion, bundling, and steric hindrance, and is responsible for the range of observed morphologies. Our model and simulations thus predict an abrupt dynamical transition between homogeneous and strongly bundled networks as a function of the actin polymerization rate. This suggests that cells may effect dramatic changes to their internal architecture through minute modifications of their nonequilibrium dynamics. Our results are consistent with available experimental data.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

## The 8-vertex model with quasi-periodic boundary conditions

### G. Niccoli

^{1}V. Terras^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.044001We study the inhomogeneous 8-vertex model (or equivalently the XYZ Heisenberg spin-1/2 chain) with all kinds of integrable quasi-periodic boundary conditions: periodic, $\sigma^x$-twisted, $\sigma^y$-twisted or $\sigma^z$-twisted. We show that in all these cases but the periodic one with an even number of sites $\mathsf{N}$, the transfer matrix of the model is related, by the vertex-IRF transformation, to the transfer matrix of the dynamical 6-vertex model with antiperiodic boundary conditions, which we have recently solved by means of Sklyanin's Separation of Variables (SOV) approach. We show moreover that, in all the twisted cases, the vertex-IRF transformation is bijective. This allows us to completely characterize, from our previous results on the antiperiodic dynamical 6-vertex model, the twisted 8-vertex transfer matrix spectrum (proving that it is simple) and eigenstates. We also consider the periodic case for $\mathsf{N}$ odd. In this case we can define two independent vertex-IRF transformations, both not bijective, and by using them we show that the 8-vertex transfer matrix spectrum is doubly degenerate, and that it can, as well as the corresponding eigenstates, also be completely characterized in terms of the spectrum and eigenstates of the dynamical 6-vertex antiperiodic transfer matrix. In all these cases we can adapt to the 8-vertex case the reformulations of the dynamical 6-vertex transfer matrix spectrum and eigenstates that had been obtained by $T$-$Q$ functional equations, where the $Q$-functions are elliptic polynomials with twist-dependent quasi-periods. Such reformulations enables one to characterize the 8-vertex transfer matrix spectrum by the solutions of some Bethe-type equations, and to rewrite the corresponding eigenstates as the multiple action of some operators on a pseudo-vacuum state, in a similar way as in the algebraic Bethe ansatz framework.

- 1. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Tensor eigenvalues and entanglement of symmetric states

### F. Bohnet-Waldraff

^{1, 2}D. Braun^{2}O. Giraud^{1}*Physical Review A*, American Physical Society, 2016, 94 (4), pp.042324- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Physikalisches Institut Tübingen

## Teleportation in an indivisible quantum system

### E. O. Kiktenko

^{1}A. K. Fedorov^{2}V. I. Man'Ko^{3, 4}*Quantum Measurements and Quantum Metrology*, 2016, 3 (1), pp.13Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.

- 1. Bauman Moscow State Technical University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MIPT - Moscow Institute of Physics and Technology [Moscow]
- 4. P. N. Lebedev Physical Institute of the Russian Academy of Sciences

## Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks

### V. Avetisov

^{1, 2}A. Gorsky^{3, 4}S. Nechaev^{5, 6}O. Valba^{1, 2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.012302We have considered an equilibrium ensemble of large Erd\H{o}s-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability, $p$. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples, $\mu$. Minimizing the system energy, we see for some positive $\mu$ formation of two predominantly unicolor clusters, linked by a "string" of $N_{bw}$ black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in emergence of a wide plateau on the $N_{bw}(\mu)$-curve, which is relevant to a spinodal decomposition in 1st order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby-universes in 2D gravity. We have conjectured that observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

- 1. The Semenov Institute of Chemical Physics
- 2. Department of Applied Mathematics
- 3. IITP - Institute for Information Transmission Problems
- 4. MIPT - Moscow Institute of Physics and Technology [Moscow]
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. P. N. Lebedev Physical Institute [Moscow]

## Spectroscopic probe of the van der Waals interaction between polar molecules and a curved surface

### Giuseppe Bimonte

^{1, 2}Thorsten Emig^{3, 4, 5}R. L. Jaffe^{6, 4}Mehran Kardar^{4}*Physical Review A*, American Physical Society, 2016, 94 (2), pp.022509- 1. Università degli studi di Napoli Federico II [Napoli]
- 2. INFN, Sezione di Napoli - Istituto Nazionale di Fisica Nucleare, Sezione di Napoli
- 3. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment
- 4. Massachussetts Institute of Technology
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. Center for Theoretical Physics and Laboratory for Nuclear Science

## Schrödinger Approach to Mean Field Games – Archive ouverte HAL

### Igor Swiecicki

^{1}Thierry Gobron^{2}Denis Ullmo^{3}#### Igor Swiecicki, Thierry Gobron, Denis Ullmo. Schrödinger Approach to Mean Field Games.

*Physical Review Letters*, American Physical Society, 2016, 116 (12), ⟨10.1103/PhysRevLett.116.128701⟩. ⟨hal-02923129⟩- 1. LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation
- 2. LPP - Laboratoire Paul Painlevé - UMR 8524
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Schrödinger approach to mean field games

### Igor Swiecicki

^{1, 2}Thierry Gobron^{1}Denis Ullmo^{2}*Physical Review Letters*, American Physical Society, 2016, 116, pp.128701Mean Field Games (MFG) provide a theoretical frame to model socio-economic systems. In this letter, we study a particular class of MFG which shows strong analogies with the {\em non-linear Schr\"odinger and Gross-Pitaevski equations} introduced in physics to describe a variety of physical phenomena ranging from deep-water waves to interacting bosons. Using this bridge many results and techniques developed along the years in the latter context can be transferred to the former. As an illustration, we study in some details an example in which the "players" in the mean field game are under a strong incentive to coordinate themselves.

- 1. LPTM - Laboratoire de Physique Théorique et Modélisation
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Scattering on two Aharonov-Bohm vortices

### Eugene Bogomolny

^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.485202The problem of two Aharonov-Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed in [J. M. Myers, J. Math. Phys. \textbf{6}, 1839 (1963)] for diffraction on a slit can be generalized to get an explicit solution for AB vortices. Due to singular nature of AB interaction the Green function and the scattering amplitude for two AB vortices obey a series of partial differential equations. Coefficients entering these equations, in their turn, fulfill ordinary non-linear differential equations whose solutions can be obtained from a solution of the Painleve V (or III) equation. The asymptotics of necessary functions for very large and very small distances between two vortices are calculated explicitly. Taken together, it means that the problem of two AB vortices is integrable.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Rich Polymorphic Behavior of Wigner Bilayers

### Moritz Antlanger

^{1, 2}Gerhard Kahl^{1}Martial Mazars^{2}Ladislav Šamaj^{3, 4}Emmanuel Trizac^{4}*Physical Review Letters*, American Physical Society, 2016, 117 (11), pp.118002- 1. Vienna University of Technology [Vienna]
- 2. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 3. Institute of Physics, Slovak Academy of Sciences
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Resonant pairing of excitons in semiconductor heterostructures

### S. V. Andreev

^{1, 2, 3}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (14), pp.140501 (1-5). <10.1103/PhysRevB.94.140501>We suggest indirect excitons in two-dimensional semiconductor heterostructures as a platform for the realization of a bosonic analog of the Bardeen-Cooper-Schrieffer superconductor. The quantum phase transition to a biexcitonic gapped state can be controlled in situ by tuning the electric field applied to the structure in the growth direction. The proposed playground should allow one to go to strongly correlated and high-temperature regimes, unattainable with Feshbach resonant atomic gases.

- 1. ITMO - National Research University of Information Technologies, Mechanics and Optics [St. Petersburg]
- 2. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Renormalized jellium model for colloidal mixtures

### María Isabel García De Soria

^{1}Carlos E. Álvarez^{2}Emmanuel Trizac^{3}*Physical Review E*, American Physical Society (APS), 2016, 94, pp.042609- 1. Fisica Teorica, Universidad de Sevilla
- 2. Universidad del Rosario, Bogota
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Rare events statistics of random walks on networks: localization and other dynamical phase transitions

### Caterina De Bacco

^{1}Alberto Guggiola^{2}Reimer Kühn^{3}Pierre Paga^{3}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.184003Rare event statistics for random walks on complex networks are investigated using the large deviations formalism. Within this formalism, rare events are realized as typical events in a suitably deformed path-ensemble, and their statistics can be studied in terms of spectral properties of a deformed Markov transition matrix. We observe two different types of phase transition in such systems: (i) rare events which are singled out for sufficiently large values of the deformation parameter may correspond to {\em localized\/} modes of the deformed transition matrix, (ii) "mode-switching transitions" may occur as the deformation parameter is varied. Details depend on the nature of the observable for which the rare event statistics is studied, as well as on the underlying graph ensemble. In the present letter we report on the statistics of the average degree of the nodes visited along a random walk trajectory in Erd\H{o}s-R\'enyi networks. Large deviations rate functions and localization properties are studied numerically. For observables of the type considered here, we also derive an analytical approximation for the Legendre transform of the large-deviations rate function, which is valid in the large connectivity limit. It is found to agree well with simulations.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. Department of Mathematics, King's College London

## Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model

### Silvio Franz

^{1}Giacomo Gradenigo^{2, 1, 3}Stefano Spigler^{1}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.032601We study how the thermodynamic properties of the Triangular Plaquette Model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in Kinetically Constrained Models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model Random-Diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "Random First-Order" kind. Finally, we give support to our conjectures studying the finite temperature phase diagram of the Random-Diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free-energy and configurational entropy can be computed by means of the cavity equations.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
- 3. CEA - CEA Saclay

## Quantumness of spin-1 states

### Fabian Bohnet-Waldraff

^{1, 2}Daniel Braun^{2}Olivier Giraud^{1}*Physical Review A*, American Physical Society, 2016, 93, pp.012104We investigate quantumness of spin-1 states, defined as the Hilbert-Schmidt distance to the convex hull of spin coherent states. We derive its analytic expression in the case of pure states as a function of the smallest eigenvalue of the Bloch matrix and give explicitly the closest classical state for an arbitrary pure state. Numerical evidence is provided that the exact formula for pure states provides an upper bound on the quantumness of mixed states. Due to the connection between quantumness and entanglement we obtain new insights into the geometry of symmetric entangled states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute für Theoretische Physik

## Quantum Levy flights and multifractality of dipolar excitations in a random system

### X. Deng

^{1}B. L. Altshuler^{2, 3}G. V. Shlyapnikov^{4, 2, 5, 6, 7}L. Santos^{1}*Physical Review Letters*, American Physical Society, 2016, 117, pp.020401We consider dipolar excitations propagating via dipole-induced exchange among immobile molecules randomly spaced in a lattice. The character of the propagation is determined by long-range hops (Levy flights). We analyze the eigen-energy spectra and the multifractal structure of the wavefunctions. In 1D and 2D all states are localized, although in 2D the localization length can be extremely large leading to an effective localization-delocalization crossover in realistic systems. In 3D all eigenstates are extended but not always ergodic, and we identify the energy intervals of ergodic and non-ergodic states. The reduction of the lattice filling induces an ergodic to non-ergodic transition, and the excitations are mostly non-ergodic at low filling.

- 1. LUH - Leibniz Universität Hannover [Hannover]
- 2. Kavli Institute for Theoretical Physics
- 3. Columbia University [New York]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 6. Russian Quantum Center
- 7. Wuhan Institute of Physics and Mathematics

## Post-processing procedure for industrial quantum key distribution systems

### Evgeny Kiktenko

^{1}Anton Trushechkin^{2}Yury Kurochkin^{3}Aleksey Fedorov^{4, 3}*Journal of Physics: Conference Series*, IOP Publishing, 2016, 741, pp.012081- 1. Bauman Moscow State Technical University
- 2. SMI - Steklov Mathematical Institute
- 3. Russian Quantum Center
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Poisson-Boltzmann thermodynamics of counter-ions confined by curved hard walls

### Ladislav Samaj

^{1}E. Trizac^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.012601We consider a set of identical mobile point-like charges (counter-ions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively 1D plates and the 2D cylinder have already been solved, the 3D sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion/explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counter-ions inside a charged sphere (salt-free system).

- 1. Institute of Physics, Slovak Academy of Sciences
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

### P. Karpov

^{1}S. Brazovskii^{2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (12), pp.125108- 1. MISIS - National University of Science and Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Phase diagram of a graphene bilayer in the zero-energy Landau level

### Angelika Knothe

^{1, 2}Thierry Jolicoeur^{2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (23), pp.235149- 1. University of Freiburg [Freiburg]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Partial transpose criteria for symmetric states

### F. Bohnet-Waldraff

^{1, 2}D. Braun^{2}O. Giraud^{1}*Physical Review A*, American Physical Society, 2016, 94 (4), pp.042343- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Eberhard Karls Universität Tübingen

## Origin of emission from square-shaped organic microlasers

### S. Bittner

^{1, 2}C. Lafargue^{2}I. Gozhyk^{2, 3}N. Djellali^{2}L. Milliet^{2}D. T. Hickox-Young^{2}C. Ulysse^{4}D. Bouche^{5}R. Dubertrand^{6}E. Bogomolny^{7}J. Zyss^{2}M. Lebental^{2}*EPL*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2016, 113, pp.54002The emission from open cavities with non-integrable features remains a challenging problem of practical as well as fundamental relevance. Square-shaped dielectric microcavities provide a favorable case study with generic implications for other polygonal resonators. We report on a joint experimental and theoretical study of square-shaped organic microlasers exhibiting a far-field emission that is strongly concentrated in the directions parallel to the side walls of the cavity. A semiclassical model for the far-field distributions is developed that is in agreement with even fine features of the experimental findings. Comparison of the model calculations with the experimental data allows the precise identification of the lasing modes and their emission mechanisms, providing strong support for a physically intuitive ray-dynamical interpretation. Special attention is paid to the role of diffraction and the finite side length.

- 1. Department of Applied Physics, Yale University
- 2. LPQM - Laboratoire de Photonique Quantique et Moléculaire
- 3. SVI - Surface du Verre et Interfaces
- 4. LPN - Laboratoire de photonique et de nanostructures
- 5. CMLA - Centre de Mathématiques et de Leurs Applications
- 6. Université de Liège
- 7. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Optomechanical many-body cooling using frustration

### Thomás Fogarty

^{1}Haggai Landa^{2}Cecilia Cormick^{3}Giovanna Morigi^{1}*Physical Review A*, American Physical Society, 2016, 94 (2), pp.023844- 1. Universität des Saarlandes [Saarbrücken]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IFEG - Instituto de Fisica Enrique Gaviola

## Optical-lattice-assisted magnetic phase transition in a spin-orbit-coupled Bose-Einstein condensate

### Giovanni I. Martone

^{1, 2, 3, 4}Tomoki Ozawa^{4}Chunlei Qu^{4}Sandro Stringari^{4}*Physical Review A*, American Physical Society, 2016, 94 (4), pp.043629- 1. Università degli studi di Bari
- 2. INFN, Sezione di Bari - Istituto Nazionale di Fisica Nucleare, Sezione di Bari
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. INO-CNR BEC - Università di Trento

## One step replica symmetry breaking and extreme order statistics of logarithmic REMs

### Xiangyu Cao

^{1}Yan V. Fyodorov^{2}Pierre Le Doussal^{3}*SciPost Physics*, 2016, 1, pp.011Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance ("ultraviolet", UV) limit, in terms of the biased minimal process. Our approach provides connections of the replica framework to results in the probability literature and sheds further light on the freezing/duality conjecture which was the source of many previous results for log-REMs. In this way we derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations) in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the second min statistics is largely independent of details of UV data, whose influence is seen only through the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of $1/f$-noise.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. School of Mathematical Sciences [London]
- 3. LPTENS - Laboratoire de Physique Théorique de l'ENS

## On the Gap and Time Interval between the First Two Maxima of Long Continuous Time Random Walks

### Philippe Mounaix

^{1}Gregory Schehr^{2}Satya N. Majumdar^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2016, pp.013303We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval $T$ where at each time step the walker waits a random time $\tau$, before performing a jump drawn from a symmetric continuous probability distribution function (PDF) $f(\eta)$, of L\'evy index $0 < \mu \leq 2$. Our study includes the case where the waiting time PDF $\Psi(\tau)$ has a power law tail, $\Psi(\tau) \propto \tau^{-1 - \gamma}$, with $0< \gamma < 1$, such that the average time between two consecutive jumps is infinite. The random motion is sub-diffusive if $\gamma < \mu/2$ (and super-diffusive if $\gamma > \mu/2$). We investigate the joint PDF of the gap $g$ between the first two highest positions of the CTRW and the time $t$ separating these two maxima. We show that this PDF reaches a stationary limiting joint distribution $p(g,t)$ in the limit of long CTRW, $T \to \infty$. Our exact analytical results show a very rich behavior of this joint PDF in the $(\gamma, \mu)$ plane, which we study in great detail. Our main results are verified by numerical simulations. This work provides a non trivial extension to CTRWs of the recent study in the discrete time setting by Majumdar et al. (J. Stat. Mech. P09013, 2014).

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## On the algebraic area of lattice walks and the Hofstadter model

### Stephane Ouvry

^{1}Stephan Wagner^{2}Shuang Wu^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.495205We consider the generating function of the algebraic area of lattice walks, evaluated at a root of unity, and its relation to the Hofstadter model. In particular, we obtain an expression for the generating function of the n-th moments of the Hofstadter Hamiltonian in terms of a complete elliptic integral, evaluated at a rational function. This in turn gives us both exact and asymptotic formulas for these moments.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Department of Mathematics [Stellenbosch]

## On determinant representations of scalar products and form factors in the SoV approach: the XXX case

### Nikolai Kitanine

^{1}J. M. Maillet^{2}G. Niccoli^{2}Véronique Terras^{3}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49 (10), pp.104002. <10.1088/1751-8113/49/10/104002 >In the present article we study the form factors of quantum integrable lattice models solvable by the separation of variables (SoVs) method. It was recently shown that these models admit universal determinant representations for the scalar products of the so-called separate states (a class which includes in particular all the eigenstates of the transfer matrix). These results permit to obtain simple expressions for the matrix elements of local operators (form factors). However, these representations have been obtained up to now only for the completely inhomogeneous versions of the lattice models considered. In this article we give a simple algebraic procedure to rewrite the scalar products (and hence the form factors) for the SoV related models as Izergin or Slavnov type determinants. This new form leads to simple expressions for the form factors in the homogeneous and thermodynamic limits. To make the presentation of our method clear, we have chosen to explain it first for the simple case of the XXX Heisenberg chain with anti-periodic boundary conditions. We would nevertheless like to stress that the approach presented in this article applies as well to a wide range of models solved in the SoV framework.

- 1. IMB - Institut de Mathématiques de Bourgogne [Dijon]
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Occupation time statistics of the random acceleration model

### Hermann Joel Ouandji Boutcheng

^{1, 2}Thomas Bouetou Bouetou^{3, 1}Theodore W. Burkhardt^{4}Alberto Rosso^{5}Andrea Zoia^{6}Kofane Timoleon Crepin^{2, 1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, pp.053213The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are non-trivial and not yet completely understood. In this paper we consider the occupation time $T_+$ of the one-dimensional random acceleration model on the positive half-axis. We calculate the first two moments of $T_+$ analytically and also study the statistics of $T_+$ with Monte Carlo simulations. One goal of our work was to ascertain whether the occupation time $T_+$ and the time $T_m$ at which the maximum of the process is attained are statistically equivalent. For regular Brownian motion the distributions of $T_+$ and $T_m$ coincide and are given by L\'evy's arcsine law. We show that for randomly accelerated motion the distributions of $T_+$ and $T_m$ are quite similar but not identical. This conclusion follows from the exact results for the moments of the distributions and is also consistent with our Monte Carlo simulations.

- 1. CETIC asbl - Centre d’Excellence en Technologies de l’Information et de la Communication
- 2. University of Yaoundé [Cameroun]
- 3. ENSP - Ecole Nationale Supérieure Polytechnique [Yaoundé]
- 4. Temple University [Philadelphia]
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. CEA-DEN - CEA-Direction de l'Energie Nucléaire

## Number statistics for β -ensembles of random matrices: Applications to trapped fermions at