# Publications 2020

## 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

## 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

## 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 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 – 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

## 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

## 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

## 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

## 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

## 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)

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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 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 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

## 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

## 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

## 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