# Publications 2021

## A tale of two (and more) altruists – Archive ouverte HAL

### B. de Bruyne

^{1}J. Randon-FurlingS. Redner#### B. de Bruyne, J. Randon-Furling, S. Redner. A tale of two (and more) altruists.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021, 2021 (10), pp.103405. ⟨10.1088/1742-5468/ac2906⟩. ⟨hal-03390680⟩We introduce a minimalist dynamical model of wealth evolution and wealth sharing among $N$ agents as a platform to compare the relative merits of altruism and individualism. In our model, the wealth of each agent independently evolves by diffusion. For a population of altruists, whenever any agent reaches zero wealth (that is, the agent goes bankrupt), the remaining wealth of the other $N-1$ agents is equally shared among all. The population is collectively defined to be bankrupt when its total wealth falls below a specified small threshold value. For individualists, each time an agent goes bankrupt (s)he is considered to be "dead" and no wealth redistribution occurs. We determine the evolution of wealth in these two societies. Altruism leads to more global median wealth at early times; eventually, however, the longest-lived individualists accumulate most of the wealth and are richer and more long lived than the altruists.

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

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

### Thibaud Maimbourg

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

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

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

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

### Davide IacobacciGiuseppe BimonteThorsten Emig

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

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

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

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

### Maxime Martinez

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

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

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

## Condensation transition and ensemble inequivalence in the discrete nonlinear Schrödinger equation – Archive ouverte HAL

### Giacomo GradenigoStefano IubiniRoberto LiviSatya N. Majumdar

^{1}Satya Majumdar^{1}#### Giacomo Gradenigo, Stefano Iubini, Roberto Livi, Satya N. Majumdar, Satya Majumdar. Condensation transition and ensemble inequivalence in the discrete nonlinear Schrödinger equation.

*European Physical Journal E: Soft matter and biological physics*, EDP Sciences: EPJ, 2021, 44 (3), ⟨10.1140/epje/s10189-021-00046-5⟩. ⟨hal-03388432⟩The thermodynamics of the discrete nonlinear Schr\"odinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a thermalized phase and a condensed (localized) one occurs at the infinite-temperature line. Inequivalence between statistical ensembles characterizes the condensed phase, where the grand-canonical representation does not apply. The control over finite size corrections of the microcanonical partition function allows to design an experimental test of delocalized negative-temperature states in lattices of cold atoms.

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

## Condensation transition in the late-time position of a run-and-tumble particle – Archive ouverte HAL

### Francesco Mori

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Grégory Schehr^{3}Pierre Le Doussal^{2}Satya Majumdar^{1}#### Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr, Pierre Le Doussal, et al.. Condensation transition in the late-time position of a run-and-tumble particle.

*Physical Review E*, American Physical Society (APS), 2021, 103 (6), ⟨10.1103/PhysRevE.103.062134⟩. ⟨hal-03301446⟩We study the position distribution $P(\vec{R},N)$ of a run-and-tumble particle (RTP) in arbitrary dimension $d$, after $N$ runs. We assume that the constant speed $v>0$ of the particle during each running phase is independently drawn from a probability distribution $W(v)$ and that the direction of the particle is chosen isotropically after each tumbling. The position distribution is clearly isotropic, $P(\vec{R},N)\to P(R,N)$ where $R=|\vec{R}|$. We show that, under certain conditions on $d$ and $W(v)$ and for large $N$, a condensation transition occurs at some critical value of $R=R_c\sim O(N)$ located in the large deviation regime of $P(R,N)$. For $R

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

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

### Tristan Gautié

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

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

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

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

### Naftali R. Smith

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

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

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

## Diffusiophoresis driven colloidal manipulation and shortcuts to adiabaticity – Archive ouverte HAL

### Parvin Bayati

^{1}Emmanuel Trizac^{1}#### Parvin Bayati, Emmanuel Trizac. Diffusiophoresis driven colloidal manipulation and shortcuts to adiabaticity.

*New Journal of Physics*, Institute of Physics: Open Access Journals, 2021, 23 (6), pp.063028. ⟨10.1088/1367-2630/abf799⟩. ⟨hal-03301439⟩While compressing a colloidal state by optical means alone has been previously achieved through a specific time-dependence of the trap stiffness, realizing quickly the reverse transformation stumbles upon the necessity of a transiently expulsive trap. To circumvent this difficulty, we propose to drive the colloids by a combination of optical trapping and diffusiophoretic forces, both time-dependent. Forcing via diffusiophoresis is enforced by controlling the salt concentration at the boundary of the domain where the colloids are confined. The method takes advantage of the separation of time scales between salt and colloidal dynamics, and realizes a fast decompression in an optical trap that remains confining at all times. We thereby obtain a so-called shortcut to adiabaticity protocol where colloidal dynamics, enslaved to salt dynamics, can nevertheless be controlled as desired.

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

## Distribution of the time of the maximum for stationary processes – Archive ouverte HAL

### Francesco Mori

^{1}Satya N. Majumdar^{1}Grégory Schehr^{2}Satya Majumdar^{1}#### Francesco Mori, Satya N. Majumdar, Grégory Schehr, Satya Majumdar. Distribution of the time of the maximum for stationary processes.

*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2021, 135 (3), pp.30003. ⟨10.1209/0295-5075/ac19ee⟩. ⟨hal-03389836⟩We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. We study the probability density function (PDF) $P(t_{\rm m}|T)$ of the time $t_{\rm m}$ at which $x(\tau)$ reaches its global maximum. By using a path integral method, we compute $P(t_{\rm m}|T)$ for a number of equilibrium and nonequilibrium stationary processes, including the Ornstein-Uhlenbeck process, Brownian motion with stochastic resetting and a single confined run-and-tumble particle. For a large class of equilibrium stationary processes that correspond to diffusion in a confining potential, we show that the scaled distribution $P(t_{\rm m}|T)$, for large $T$, has a universal form (independent of the details of the potential). This universal distribution is uniform in the ``bulk'', i.e., for $0 \ll t_{\rm m} \ll T$ and has a nontrivial edge scaling behavior for $t_{\rm m} \to 0$ (and when $t_{\rm m} \to T$), that we compute exactly. Moreover, we show that for any equilibrium process the PDF $P(t_{\rm m}|T)$ is symmetric around $t_{\rm m}=T/2$, i.e., $P(t_{\rm m}|T)=P(T-t_{\rm m}|T)$. This symmetry provides a simple method to decide whether a given stationary time series $x(\tau)$ is at equilibrium or not.

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

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

### Valentina Ros

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

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

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

## Dynamical phase transition in the first-passage probability of a Brownian motion – Archive ouverte HAL

### Benjamin Besga

^{1}Felix Faisant^{1}Artyom Petrosyan^{1}Sergio Ciliberto^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}#### Benjamin Besga, Felix Faisant, Artyom Petrosyan, Sergio Ciliberto, Satya N. Majumdar, et al.. Dynamical phase transition in the first-passage probability of a Brownian motion.

*Physical Review E*, American Physical Society (APS), 2021, 104 (1), ⟨10.1103/PhysRevE.104.L012102⟩. ⟨hal-03301450⟩We study theoretically, experimentally and numerically the probability distribution $F(t_f|x_0,L)$ of the first passage times $t_f$ needed by a freely diffusing Brownian particle to reach a target at a distance $L$ from the initial position $x_0$, taken from a normalized distribution $(1/\sigma)\, g(x_0/\sigma)$ of finite width $\sigma$. We show the existence of a critical value $b_c$ of the parameter $b=L/\sigma$, which determines the shape of $F(t_f|x_0,L)$. For $b>b_c$ the distribution $F(t_f|x_0,L)$ has a maximum and a minimum whereas for $b

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

## Dynamics of Nanoparticles in Polydisperse Polymer Networks: from Free Diffusion to Hopping – Archive ouverte HAL

### Valerio Sorichetti

^{1, 2, 3}Virginie Hugouvieux^{2}Walter Kob^{1}#### Valerio Sorichetti, Virginie Hugouvieux, Walter Kob. Dynamics of Nanoparticles in Polydisperse Polymer Networks: from Free Diffusion to Hopping.

*Macromolecules*, American Chemical Society, 2021, 54 (18), pp.8575-8589. ⟨10.1021/acs.macromol.1c01394⟩. ⟨hal-03358744⟩- 1. L2C - Laboratoire Charles Coulomb
- 2. UMR IATE - Ingénierie des Agro-polymères et Technologies Émergentes
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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

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

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

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

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

## Exclusion statistics for particles with a discrete spectrum – Archive ouverte HAL

### Stéphane Ouvry

^{1}Alexios.P. Polychronakos#### Stéphane Ouvry, Alexios.P. Polychronakos. Exclusion statistics for particles with a discrete spectrum.

*Nucl.Phys.B*, 2021, 972, pp.115573. ⟨10.1016/j.nuclphysb.2021.115573⟩. ⟨hal-03261998⟩We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a relation with the Ramanujan continued fraction identity and appropriate generalizations.

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

## Expected maximum of bridge random walks & L\’evy flights – Archive ouverte HAL

### Benjamin de Bruyne

^{1}Satya N. Majumdar^{1}Gregory Schehr^{2}#### Benjamin de Bruyne, Satya N. Majumdar, Gregory Schehr. Expected maximum of bridge random walks & L\'evy flights.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03388319⟩We consider one-dimensional discrete-time random walks (RWs) with arbitrary symmetric and continuous jump distributions $f(\eta)$, including the case of L\'evy flights. We study the expected maximum ${\mathbb E}[M_n]$ of bridge RWs, i.e., RWs starting and ending at the origin after $n$ steps. We obtain an exact analytical expression for ${\mathbb E}[M_n]$ valid for any $n$ and jump distribution $f(\eta)$, which we then analyze in the large $n$ limit up to second leading order term. For jump distributions whose Fourier transform behaves, for small $k$, as $\hat f(k) \sim 1 - |a\, k|^\mu$ with a L\'evy index $0<\mu \leq 2$ and an arbitrary length scale $a>0$, we find that, at leading order for large $n$, ${\mathbb E}[M_n]\sim a\, h_1(\mu)\, n^{1/\mu}$. We obtain an explicit expression for the amplitude $h_1(\mu)$ and find that it carries the signature of the bridge condition, being different from its counterpart for the free random walk. For $\mu=2$, we find that the second leading order term is a constant, which, quite remarkably, is the same as its counterpart for the free RW. For generic $0< \mu < 2$, this second leading order term is a growing function of $n$, which depends non-trivially on further details of $\hat f (k)$, beyond the L\'evy index $\mu$. Finally, we apply our results to compute the mean perimeter of the convex hull of the $2d$ Rouse polymer chain and of the $2d$ run-and-tumble particle, as well as to the computation of the survival probability in a bridge version of the well-known "lamb-lion" capture problem.

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

## First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension – Archive ouverte HAL

### Francesco Mori

^{1}Giacomo GradenigoSatya N. Majumdar^{1}Satya Majumdar^{1}#### Francesco Mori, Giacomo Gradenigo, Satya N. Majumdar, Satya Majumdar. First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021, 2021 (10), pp.103208. ⟨10.1088/1742-5468/ac2899⟩. ⟨hal-03389892⟩We consider a single run-and-tumble particle (RTP) moving in one dimension. We assume that the velocity of the particle is drawn independently at each tumbling from a zero-mean Gaussian distribution and that the run times are exponentially distributed. We investigate the probability distribution $P(X,N)$ of the position $X$ of the particle after $N$ runs, with $N\gg 1$. We show that in the regime $ X \sim N^{3/4}$ the distribution $P(X,N)$ has a large deviation form with a rate function characterized by a discontinuous derivative at the critical value $X=X_c>0$. The same is true for $X=-X_c$ due to the symmetry of $P(X,N)$. We show that this singularity corresponds to a first-order condensation transition: for $X>X_c$ a single large jump dominates the RTP trajectory. We consider the participation ratio of the single-run displacements as the order parameter of the system, showing that this quantity is discontinuous at $X=X_c$. Our results are supported by numerical simulations performed with a constrained Markov chain Monte Carlo algorithm.

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

## Fluctuation-driven transitions in localized insulators: Intermittent metallicity and path chaos precede delocalization – Archive ouverte HAL

### Valentina Ros

^{1}Markus Müller#### Valentina Ros, Markus Müller. Fluctuation-driven transitions in localized insulators: Intermittent metallicity and path chaos precede delocalization.

*Physical Review B*, American Physical Society, 2021, 104 (9), ⟨10.1103/PhysRevB.104.094205⟩. ⟨hal-03389793⟩We study how interacting localized degrees of freedom are affected by slow thermal fluctuations that change the effective local disorder. We compute the time-averaged (annealed) conductance in the insulating regime and find three distinct insulating phases, separated by two transitions. The first occurs between a non-resonating insulator and an intermittent metal. The average conductance is always dominated by rare temporal fluctuations. However, in the intermittent metal, they are so strong that the system becomes metallic for an exponentially small fraction of the time. A second transition occurs within that phase. At stronger disorder, there is a single optimal path providing the dominant contribution to the conductance at all times, but closer to delocalization, a transition to a phase with fluctuating paths occurs. This last phase displays the quantum analogon of configurational chaos in glassy systems in that thermal fluctuations induce significant changes of the dominant decay channels. While in the insulator the annealed conductance is strictly bigger than the conductance with typical, frozen disorder, we show that the threshold to delocalization is insensitive to whether or not thermal fluctuations are admitted. This rules out a potential bistability, at fixed disorder, of a localized phase with suppressed internal fluctuations and a delocalized, internally fluctuating phase.

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

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

### Eugene Bogomolny

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

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

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

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

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

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

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

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

## Generating constrained run-and-tumble trajectories – Archive ouverte HAL

### Benjamin de Bruyne

^{1}Satya N. Majumdar^{1}Grégory Schehr^{2}Satya Majumdar^{1}#### Benjamin de Bruyne, Satya N. Majumdar, Grégory Schehr, Satya Majumdar. Generating constrained run-and-tumble trajectories.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2021, 54 (38), pp.385004. ⟨10.1088/1751-8121/ac1d8e⟩. ⟨hal-03388311⟩We propose a method to exactly generate bridge run-and-tumble trajectories that are constrained to start at the origin with a given velocity and to return to the origin after a fixed time with another given velocity. The method extends the concept of effective Langevin equations, valid for Markovian stochastic processes such as Brownian motion, to a non-Markovian stochastic process driven by a telegraphic noise, with exponentially decaying correlations. We obtain effective space-time dependent tumbling rates that implicitly accounts for the bridge constraint. We extend the method to other types of constrained run-and-tumble particles such as excursions and meanders. The method is implemented numerically and is shown to be very efficient.

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

## Generating discrete-time constrained random walks and Lévy flights – Archive ouverte HAL

### Benjamin de Bruyne

^{1}Satya N. Majumdar^{1}Grégory Schehr^{2}Satya Majumdar^{1}#### Benjamin de Bruyne, Satya N. Majumdar, Grégory Schehr, Satya Majumdar. Generating discrete-time constrained random walks and Lévy flights.

*Physical Review E*, American Physical Society (APS), 2021, 104 (2), ⟨10.1103/PhysRevE.104.024117⟩. ⟨hal-03388308⟩We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method is based on an effective jump distribution that implicitly accounts for the bridge constraint. It is illustrated on various jump distributions and is shown to be very efficient in practice. In addition, we show how to generalize the method to other types of constrained random walks such as generalized bridges, excursions, and meanders.

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

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

### Giampaolo Folena

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

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

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

## Hamiltonian and exclusion statistics approach to discrete forward-moving paths – Archive ouverte HAL

### Stéphane Ouvry

^{1}Alexios P. Polychronakos#### Stéphane Ouvry, Alexios P. Polychronakos. Hamiltonian and exclusion statistics approach to discrete forward-moving paths.

*Phys.Rev.E*, 2021, 104 (1), pp.014143. ⟨10.1103/PhysRevE.104.014143⟩. ⟨hal-03197542⟩We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for paths with arbitrary starting and ending points, expressing it as a rational combination of determinants. Exploiting a connection between random walks and quantum exclusion statistics that we previously established, we express this generating function in terms of grand partition functions for exclusion particles in a finite harmonic spectrum and present an alternative, simpler form for its logarithm that makes its polynomial structure explicit.

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

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

### A. Pricoupenko

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

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

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

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

### David S. Dean

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

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

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

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

### Pierre Le Doussal

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

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

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

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

### Xiangyu Cao

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

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

## Local structure of DNA toroids reveals curvature-dependent intermolecular forces – Archive ouverte HAL

### Luca Barberi

^{1}Françoise Livolant^{2}Amélie Leforestier^{2}Martin Lenz^{1}#### Luca Barberi, Françoise Livolant, Amélie Leforestier, Martin Lenz. Local structure of DNA toroids reveals curvature-dependent intermolecular forces.

*Nucleic Acids Research*, Oxford University Press, 2021, 49 (7), pp.3709-3718. ⟨10.1093/nar/gkab197⟩. ⟨hal-03365453⟩Abstract In viruses and cells, DNA is closely packed and tightly curved thanks to polyvalent cations inducing an effective attraction between its negatively charged filaments. Our understanding of this effective attraction remains very incomplete, partly because experimental data is limited to bulk measurements on large samples of mostly uncurved DNA helices. Here we use cryo electron microscopy to shed light on the interaction between highly curved helices. We find that the spacing between DNA helices in spermine-induced DNA toroidal condensates depends on their location within the torus, consistent with a mathematical model based on the competition between electrostatic interactions and the bending rigidity of DNA. We use our model to infer the characteristics of the interaction potential, and find that its equilibrium spacing strongly depends on the curvature of the filaments. In addition, the interaction is much softer than previously reported in bulk samples using different salt conditions. Beyond viruses and cells, our characterization of the interactions governing DNA-based dense structures could help develop robust designs in DNA nanotechnologies.

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

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

### Giacomo GradenigoStefano IubiniRoberto LiviSatya N. Majumdar

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

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

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

## Many-body quantum Zeno effect and measurement-induced subradiance transition – Archive ouverte HAL

### Alberto Biella

^{1}Marco Schiró^{2, 3}#### Alberto Biella, Marco Schiró. Many-body quantum Zeno effect and measurement-induced subradiance transition.

*Quantum*, Verein, 2021, 5, pp.528. ⟨10.22331/q-2021-08-19-528⟩. ⟨hal-03388410⟩It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. JEIPCdF - Jeunes Équipes de l'Institut de Physique du Collège de France
- 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

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

### Satya N. Majumdar

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

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

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

## Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks – Archive ouverte HAL

### Xhek Turkeshi

^{1}Alberto Biella^{2}Rosario Fazio^{1}Marcello Dalmonte^{1}Marco Schiró^{3}#### Xhek Turkeshi, Alberto Biella, Rosario Fazio, Marcello Dalmonte, Marco Schiró. Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks.

*Physical Review B*, American Physical Society, 2021, 103 (22), ⟨10.1103/PhysRevB.103.224210⟩. ⟨hal-03301454⟩We investigate measurement-induced phase transitions in the Quantum Ising chain coupled to a monitoring environment. We compare two different limits of the measurement problem, the stochastic quantum-state diffusion protocol corresponding to infinite small jumps per unit of time and the no-click limit, corresponding to post-selection and described by a non-Hermitian Hamiltonian. In both cases we find a remarkably similar phenomenology as the measurement strength $\gamma$ is increased, namely a sharp transition from a critical phase with logarithmic scaling of the entanglement to an area-law phase, which occurs at the same value of the measurement rate in the two protocols. An effective central charge, extracted from the logarithmic scaling of the entanglement, vanishes continuously at the common transition point, although with different critical behavior possibly suggesting different universality classes for the two protocols. We interpret the central charge mismatch near the transition in terms of noise-induced disentanglement, as suggested by the entanglement statistics which displays emergent bimodality upon approaching the critical point. The non-Hermitian Hamiltonian and its associated subradiance spectral transition provide a natural framework to understand both the extended critical phase, emerging here for a model which lacks any continuous symmetry, and the entanglement transition into the area law.

- 1. ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. JEIPCdF - Jeunes Équipes de l'Institut de Physique du Collège de France

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

### P. NaidonD. s. Petrov

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

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

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

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

### Manas Kulkarni

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

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

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

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

### Carlos A. Plata

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

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

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

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

### Eoin Quinn

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

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

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

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

### Jacek GrelaSatya N. Majumdar

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

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

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

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

### Eoin Quinn

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

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

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

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

### Lucas Varela

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

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

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

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

### B. de Bruyne

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

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

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

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

### Lorenzo Gotta

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

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

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

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

### Serguei Brazovskii

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

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

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

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

### David S. Dean

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

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

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

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

### Antonio Sclocchi

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

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

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

## Quantitative Analysis of Shock Wave Dynamics in a Fluid of Light – Archive ouverte HAL

### T. Bienaimé

^{1}M. Isoard^{2}Q. Fontaine^{1}A. Bramati^{1}A. m. Kamchatnov^{3}Q. Glorieux^{1}N. Pavloff^{2}#### T. Bienaimé, M. Isoard, Q. Fontaine, A. Bramati, A. m. Kamchatnov, et al.. Quantitative Analysis of Shock Wave Dynamics in a Fluid of Light.

*Physical Review Letters*, American Physical Society, 2021, 126 (18), ⟨10.1103/PhysRevLett.126.183901⟩. ⟨hal-03301435⟩We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge of the shock, as well as the location of the nonlinear oscillations are well described by recent developments of Whitham modulation theory. Our work constitutes a detailed and accurate benchmark for this approach. It opens exciting possibilities to engineer specific configurations of optical shock wave for studying wave-mean flow interaction.

- 1. LKB (Jussieu) - Laboratoire Kastler Brossel
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institute for Spectroscopy RAS

## Relaxation dynamics of two interacting electrical double-layers in a 1D Coulomb system – Archive ouverte HAL

### Lucas Varela

^{1}Sergio AndrausEmmanuel Trizac^{1}Gabriel Téllez#### Lucas Varela, Sergio Andraus, Emmanuel Trizac, Gabriel Téllez. Relaxation dynamics of two interacting electrical double-layers in a 1D Coulomb system.

*Journal of Physics: Condensed Matter*, IOP Publishing, 2021. ⟨hal-03301761⟩We consider an out-of-equilibrium one-dimensional model for two electrical double-layers. With a combination of exact calculations and Brownian Dynamics simulations, we compute the relaxation time ($\tau$) for an electroneutral salt-free suspension, made up of two fixed colloids, with $N$ neutralizing mobile counterions. For $N$ odd, the two double-layers never decouple, irrespective of their separation $L$; this is the regime of like-charge attraction, where $\tau$ exhibits a diffusive scaling in $L^2$ for large $L$. On the other hand, for even $N$, $L$ no longer is the relevant length scale for setting the relaxation time; this role is played by the Bjerrum length. This leads to distinctly different dynamics: for $N$ even, thermal effects are detrimental to relaxation, increasing $\tau$, while they accelerate relaxation for $N$ odd. Finally, we also show that the mean-field theory is recovered for large $N$ and moreover, that it remains an operational treatment down to relatively small values of $N$ ($N>3$).

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

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

### Vittorio ErbaMauro Pastore

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

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

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

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

### Clément Le PriolPierre Le Doussal

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

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

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

## Stationary nonequilibrium bound state of a pair of run and tumble particles – Archive ouverte HAL

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Grégory Schehr^{3}Pierre Le Doussal^{1}Satya Majumdar^{2}#### Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr, Pierre Le Doussal, Satya Majumdar. Stationary nonequilibrium bound state of a pair of run and tumble particles.

*Physical Review E*, American Physical Society (APS), 2021, 104 (4), ⟨10.1103/PhysRevE.104.044103⟩. ⟨hal-03389938⟩We study two interacting identical run and tumble particles (RTP's) in one dimension. Each particle is driven by a telegraphic noise, and in some cases, also subjected to a thermal white noise with a corresponding diffusion constant $D$. We are interested in the stationary bound state formed by the two RTP's in the presence of a mutual attractive interaction. The distribution of the relative coordinate $y$ indeed reaches a steady state that we characterize in terms of the solution of a second-order differential equation. We obtain the explicit formula for the stationary probability $P(y)$ of $y$ for two examples of interaction potential $V(y)$. The first one corresponds to $V(y) \sim |y|$. In this case, for $D=0$ we find that $P(y)$ contains a delta function part at $y=0$, signaling a strong clustering effect, together with a smooth exponential component. For $D>0$, the delta function part broadens, leading instead to weak clustering. The second example is the harmonic attraction $V(y) \sim y^2$ in which case, for $D=0$, $P(y)$ is supported on a finite interval. We unveil an interesting relation between this two-RTP model with harmonic attraction and a three-state single RTP model in one dimension, as well as with a four-state single RTP model in two dimensions. We also provide a general discussion of the stationary bound state, including examples where it is not unique, e.g., when the particles cannot cross due to an additional short-range repulsion.

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

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

### Eugene Bogomolny

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

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

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

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

### Giovanni I. MartoneAlessio RecatiNicolas Pavloff

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

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

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

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

### Silvio Franz

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

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

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

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

### Benjamin de Bruyne

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

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

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

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

### A. Bilen

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

*Physical Review Research*, American Physical Society, 2021, 3, pp.L022023. ⟨10.1103/PhysRevResearch.3.L022023⟩. ⟨hal-03160414⟩Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension $\Delta_q$ is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation \mbox{$\Delta_q=\Delta_{1-q}$} is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that the reason for this is the presence of atypically small eigenfunction amplitudes induced by two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.

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

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

### Lenart Zadnik

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

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

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

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

### Anthony Mays

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

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

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

## Truncated linear statistics in the one dimensional one-component plasma – Archive ouverte HAL

### Ana Flack

^{1}Satya N. Majumdar^{1}Grégory Schehr^{2}Satya Majumdar^{1}#### Ana Flack, Satya N. Majumdar, Grégory Schehr, Satya Majumdar. Truncated linear statistics in the one dimensional one-component plasma.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2021, 54 (43), pp.435002. ⟨10.1088/1751-8121/ac2599⟩. ⟨hal-03390705⟩In this paper, we study the probability distribution of the observable $s = (1/N)\sum_{i=N-N'+1}^N x_i$, with $1 \leq N' \leq N$ and $x_1

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

## Twist-induced local curvature of filaments in DNA toroids – Archive ouverte HAL

### L Barberi

^{1}Martin Lenz^{1, 2}#### L Barberi, Martin Lenz. Twist-induced local curvature of filaments in DNA toroids.

*Il Nuovo cimento della Societa italiana di fisica. C*, Springer-Verlag, 2021, 44, ⟨10.1393/ncc/i2021-21123-5⟩. ⟨hal-03365518⟩DNA toroidal bundles form upon condensation of one or multiple DNA filaments. DNA filaments in toroidal bundles are hexagonally packed, and collectively twist around the center line of the toroid. In a previous study, we and our coworkers argue that the filaments’ curvature locally correlates with their density in the bundle, with the filaments less closely packed where their curvature is higher. We base our claim on the assumption that twist has a negligible effect on the local curvature of filaments in DNA toroids. However, this remains to be proven. We fill this gap here, by calculating the distribution of filaments’ curvature in a geometric model of twisted toroidal bundle, which we use to describe DNA toroids by an appropriate choice of parameters. This allows us to substantiate our previous study and suggest directions for future experiments.

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

## Two-fluid coexistence and phase separation in a one-dimensional model with pair hopping and density interactions – Archive ouverte HAL

### Lorenzo Gotta

^{1}Leonardo Mazza^{1}Pascal Simon^{2}Guillaume Roux^{1}#### Lorenzo Gotta, Leonardo Mazza, Pascal Simon, Guillaume Roux. Two-fluid coexistence and phase separation in a one-dimensional model with pair hopping and density interactions.

*Physical Review B*, American Physical Society, 2021, 104 (9), ⟨10.1103/PhysRevB.104.094521⟩. ⟨hal-03389971⟩We compute the phase diagram of a one-dimensional model of spinless fermions with pair-hopping and nearest-neighbor interaction, first introduced by Ruhman and Altman, using the density-matrix renormalization group combined with various analytical approaches. Although the main phases are a Luttinger liquid of fermions and a Luttinger liquid of pairs, we also find remarkable phases in which only a fraction of the fermions are paired. In such case, two situations arise: either fermions and pairs coexist spatially in a two-fluid mixture, or they are spatially segregated leading to phase separation. These results are supported by several analytical models that describe in an accurate way various relevant cuts of the phase diagram. Last, we identify relevant microscopic observables that capture the presence of these two fluids: while originally introduced in a phenomenological way, they support a wider application of two-fluid models for describing pairing phenomena.

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

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

### Lorenzo Gotta

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

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

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

## Unifying Theory for Casimir Forces: Bulk and Surface Formulations – Archive ouverte HAL

### Giuseppe BimonteThorsten Emig

^{1}#### Giuseppe Bimonte, Thorsten Emig. Unifying Theory for Casimir Forces: Bulk and Surface Formulations.

*Universe*, 2021, 7 (7), pp.225. ⟨10.3390/universe7070225⟩. ⟨hal-03314716⟩The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula.

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

## Universal record statistics for random walks and L\’evy flights with a nonzero staying probability – Archive ouverte HAL

### Satya N. Majumdar

^{1}Philippe Mounaix^{2}Gregory Schehr^{3}#### Satya N. Majumdar, Philippe Mounaix, Gregory Schehr. Universal record statistics for random walks and L\'evy flights with a nonzero staying probability.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2021. ⟨hal-03301563⟩We compute exactly the statistics of the number of records in a discrete-time random walk model on a line where the walker stays at a given position with a nonzero probability $0\leq p \leq 1$, while with the complementary probability $1-p$, it jumps to a new position with a jump length drawn from a continuous and symmetric distribution $f_0(\eta)$. We have shown that, for arbitrary $p$, the statistics of records up to step $N$ is completely universal, i.e., independent of $f_0(\eta)$ for any $N$. We also compute the connected two-time correlation function $C_p(m_1, m_2)$ of the record-breaking events at times $m_1$ and $m_2$ and show it is also universal for all $p$. Moreover, we demonstrate that $C_p(m_1, m_2)< C_0(m_1, m_2)$ for all $p>0$, indicating that a nonzero $p$ induces additional anti-correlations between record events. We further show that these anti-correlations lead to a drastic reduction in the fluctuations of the record numbers with increasing $p$. This is manifest in the Fano factor, i.e. the ratio of the variance and the mean of the record number, which we compute explicitly. We also show that an interesting scaling limit emerges when $p \to 1$, $N \to \infty$ with the product $t = (1-p)\, N$ fixed. We compute exactly the associated universal scaling functions for the mean, variance and the Fano factor of the number of records in this scaling limit. .

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

## Universal record statistics for random walks and Lévy flights with a nonzero staying probability – Archive ouverte HAL

### Satya N Majumdar

^{1}Philippe Mounaix^{2}Gregory Schehr^{3}#### Satya N Majumdar, Philippe Mounaix, Gregory Schehr. Universal record statistics for random walks and Lévy flights with a nonzero staying probability.

*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics, 2021, 54 (31), pp.315002. ⟨10.1088/1751-8121/ac0a2f⟩. ⟨hal-03351961⟩We compute exactly the statistics of the number of records in a discrete-time random walk model on a line where the walker stays at a given position with a nonzero probability 0 p 1, while with the complementary probability 1 p, it jumps to a new position with a jump length drawn from a continuous and symmetric distribution f 0 (⌘). We have shown that, for arbitrary p, the statistics of records up to step N is completely universal, i.e., independent of f 0 (⌘) for any N. We also compute the connected two-time correlation function C p (m 1 , m 2) of the record-breaking events at times m 1 and m 2 and show it is also universal for all p. Moreover, we demonstrate that C p (m 1 , m 2) < C 0 (m 1 , m 2) for all p > 0, indicating that a nonzero p induces additional anticorrelations between record events. We further show that these anti-correlations lead to a drastic reduction in the fluctuations of the record numbers with increasing p. This is manifest in the Fano factor, i.e. the ratio of the variance and the mean of the record number, which we compute explicitly. We also show that an interesting scaling limit emerges when p ! 1, N ! 1 with the product t = (1 p) N fixed. We compute exactly the associated universal scaling functions for the mean, variance and the Fano factor of the number of records in this scaling limit.

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

## Wigner function for noninteracting fermions in hard wall potentials – Archive ouverte HAL

### Benjamin de Bruyne

^{1}David S. Dean^{2}Pierre Le Doussal^{3}Satya N. Majumdar^{1}Gregory Schehr^{4}#### Benjamin de Bruyne, David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr. Wigner function for noninteracting fermions in hard wall potentials.

*Physical Review A*, American Physical Society 2021. ⟨hal-03301503⟩The Wigner function $W_N({\bf x}, {\bf p})$ is a useful quantity to characterize the quantum fluctuations of an $N$-body system in its phase space. Here we study $W_N({\bf x}, {\bf p})$ for $N$ noninteracting spinless fermions in a $d$-dimensional spherical hard box of radius $R$ at temperature $T=0$. In the large $N$ limit, the local density approximation (LDA) predicts that $W_N({\bf x}, {\bf p}) \approx 1/(2 \pi \hbar)^d$ inside a finite region of the $({\bf x}, {\bf p})$ plane, namely for $|{\bf x}| < R$ and $|{\bf p}| < k_F$ where $k_F$ is the Fermi momentum, while $W_N({\bf x}, {\bf p})$ vanishes outside this region, or "droplet", on a scale determined by quantum fluctuations. In this paper we investigate systematically, in this quantum region, the structure of the Wigner function along the edge of this droplet, called the Fermi surf. In one dimension, we find that there are three distinct edge regions along the Fermi surf and we compute exactly the associated nontrivial scaling functions in each regime. We also study the momentum distribution $\hat \rho_N(p)$ and find a striking algebraic tail for very large momenta $\hat \rho_N(p) \propto 1/p^4$, well beyond $k_F$, reminiscent of a similar tail found in interacting quantum systems (discussed in the context of Tan's relation). We then generalize these results to higher $d$ and find, remarkably, that the scaling function close to the edge of the box is universal, i.e., independent of the dimension~$d$.

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