# Publications 2019

## A consistent quadratic curvature-tilt theory for fluid lipid membranes – Archive ouverte HAL

### M. Mert Terzi

^{1}Muhammed Ergüder^{2}Markus Deserno^{2}#### M. Mert Terzi, Muhammed Ergüder, Markus Deserno. A consistent quadratic curvature-tilt theory for fluid lipid membranes.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 151 (16), pp.164108. ⟨10.1063/1.5119683⟩. ⟨hal-02512290⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CMU - Carnegie Mellon University [Pittsburgh]

## Archive ouverte HAL – 4 π and 8 π dual Josephson effects induced by symmetry defects

### Corneliu Malciu

^{1}Leonardo Mazza^{2}Christophe Mora^{1}#### Corneliu Malciu, Leonardo Mazza, Christophe Mora. 4 π and 8 π dual Josephson effects induced by symmetry defects.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 99 (12), ⟨10.1103/PhysRevB.99.125153⟩. ⟨hal-02102139⟩In topological insulator edges, the duality between the Zeeman field orientation and the proximitized superconducting phase has been recently exploited to predict a magneto-Josephson effect with a 4$\pi$ periodicity. We revisit this latter Josephson effect in the light of this duality and show that the same 4$\pi$ quantum anomaly occurs when bridging two spinless Thouless pumps to a p-wave superconducting region that could be as small as a single and experimentally-relevant superconducting quantum dot - a point-like defect. This interpretation as a dual Josephson effect never requires the presence of Majorana modes but rather builds on the topological properties of adiabatic quantum pumps with Z topological invariants. It allows for the systematic construction of dual Josephson effects of arbitrary periodicity, such as 4$\pi$ and 8$\pi$, by using point-like defects whose symmetry differs from that of the pump, dubbed symmetry defects. Although adiabatic quantum pumps are typically discussed via mappings to two-dimensional geometries, we show that this phenomenology does not have any counterpart in conventional two-dimensional systems.

- 1. LPA - Laboratoire Pierre Aigrain
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – A consistent quadratic curvature-tilt theory for fluid lipid membranes

### M. Mert Terzi

^{1}Muhammed Ergüder^{2}Markus Deserno^{2}#### M. Mert Terzi, Muhammed Ergüder, Markus Deserno. A consistent quadratic curvature-tilt theory for fluid lipid membranes.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 151 (16), pp.164108. ⟨10.1063/1.5119683⟩. ⟨hal-02512290⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CMU - Carnegie Mellon University [Pittsburgh]

## Archive ouverte HAL – A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle

### Giacomo Gradenigo

^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}#### Giacomo Gradenigo, Satya N. Majumdar, Satya Majumdar. A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (5), pp.053206. ⟨10.1088/1742-5468/ab11be⟩. ⟨hal-02291859⟩We study the probability distribution $P(X_N=X,N)$ of the total displacement $X_N$ of an $N$-step run and tumble particle on a line, in presence of a constant nonzero drive $E$. While the central limit theorem predicts a standard Gaussian form for $P(X,N)$ near its peak, we show that for large positive and negative $X$, the distribution exhibits anomalous large deviation forms. For large positive $X$, the associated rate function is nonanalytic at a critical value of the scaled distance from the peak where its first derivative is discontinuous. This signals a first-order dynamical phase transition from a homogeneous `fluid' phase to a `condensed' phase that is dominated by a single large run. A similar first-order transition occurs for negative large fluctuations as well. Numerical simulations are in excellent agreement with our analytical predictions.

- 1. LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – A super-resolution platform for correlative live single-molecule imaging and STED microscopy

### V. InavalliMartin Lenz

^{1}Corey Butler^{2}Julie Angibaud^{3}Benjamin Compans^{4}Florian Levet^{5}Jan TønnesenOlivier Rossier^{2}Gregory Giannone^{2}Olivier Thoumine^{6}Eric Hosy^{2}Daniel Choquet^{6}Jean-Baptiste Sibarita^{2}U. Valentin Nägerl^{2}#### V. Inavalli, Martin Lenz, Corey Butler, Julie Angibaud, Benjamin Compans, et al.. A super-resolution platform for correlative live single-molecule imaging and STED microscopy.

*Nature Methods*, Nature Publishing Group, 2019, ⟨10.1038/s41592-019-0611-8⟩. ⟨hal-02348164⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IINS - Interdisciplinary Institute for Neuroscience
- 3. U1064 Inserm - CRTI - Centre de Recherche en Transplantation et Immunologie
- 4. Interdisciplinary Institute for Neuroscience
- 5. LaBRI - Laboratoire Bordelais de Recherche en Informatique
- 6. PCS - Physiologie cellulaire de la synapse

## Archive ouverte HAL – Actin dynamics drive cell-like membrane deformation

### Camille Simon

^{1}Rémy KustersValentina Caorsi^{2}Antoine AllardMajdouline Abou-Ghali^{3}John Manzi^{3}Aurelie Di Cicco^{3}Daniel Lévy^{4}Martin Lenz^{5}Jean-Francois Joanny^{3}Clément Campillo^{6}Julie Plastino^{3}Pierre Sens^{3}Cécile Sykes^{7}#### Camille Simon, Rémy Kusters, Valentina Caorsi, Antoine Allard, Majdouline Abou-Ghali, et al.. Actin dynamics drive cell-like membrane deformation.

*Nature Physics*, Nature Publishing Group, 2019, 15 (6), pp.602-609. ⟨10.1038/s41567-019-0464-1⟩. ⟨hal-02148264⟩Cell membrane deformations are crucial for proper cell function. Specialized protein assemblies initiate inward or outward membrane deformations that the cell uses respectively to uptake external substances or probe the environment. The assembly and dynamics of the actin cytoskeleton are involved in this process, although their detailed role remains controversial. We show here that a dynamic, branched actin network is sufficient to initiate both inward and outward membrane deformation. The polymerization of a dense actin network at the membrane of liposomes produces inward membrane bending at low tension , while outward deformations are robustly generated regardless of tension. Our results shed light on the mechanism cells use to internalize material , both in mammalian cells, where actin polymerization forces are required when membrane tension is increased, and in yeast, where those forces are necessary to overcome the opposing turgor pressure. By combining experimental observations with physical modelling, we propose a mechanism that explains how membrane tension and the architecture of the actin network regulate cell-like membrane deformations.

- 1. LPS - Laboratoire de Psychologie Sociale
- 2. INSP - Institut des Nanosciences de Paris
- 3. PCC - Physico-Chimie-Curie
- 4. Chercheur indépendant
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LAMBE - UMR 8587 - Laboratoire Analyse et Modélisation pour la Biologie et l'Environnement
- 7. UPMC - Université Pierre et Marie Curie - Paris 6

## Archive ouverte HAL – Anderson-like localization transition of random walks with resetting

### Denis Boyer

^{1}Andrea Falcón-Cortés^{2}Luca Giuggioli^{3}Satya N. Majumdar^{4}Satya Majumdar^{4}#### Denis Boyer, Andrea Falcón-Cortés, Luca Giuggioli, Satya N. Majumdar, Satya Majumdar. Anderson-like localization transition of random walks with resetting.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (5), pp.053204. ⟨10.1088/1742-5468/ab16c2⟩. ⟨hal-02291906⟩We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized phase settles above a critical resetting rate, or rate of memory use, and the probability density asymptotically adopts in this regime a non-equilibrium steady state similar to that of the well known problem of diffusion with resetting to the origin. The transition occurs because of the presence of a single impurity site where the resetting rate is lower than on other sites, and around which the walker spontaneously localizes. Near criticality, the localization length diverges with a critical exponent that falls in the same class as the self-consistent theory of Anderson localization of waves in random media. The critical dimensions are also the same in both problems. Our study provides analytically tractable examples of localization transitions in path-dependent, reinforced stochastic processes, which can be also useful for understanding spatial learning by living organisms.

- 1. Instituto de Fisica
- 2. UNAM - Universidad Nacional Autónoma de México
- 3. University of Bristol [Bristol]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Anyonic tight-binding models of parafermions and of fractionalized fermions

### Davide RossiniMatteo CarregaMarcello Calvanese StrinatiLeonardo Mazza

^{1}*Phys.Rev.B*, 2019, 99 (8), pp.085113. 〈10.1103/PhysRevB.99.085113〉Parafermions are emergent quasiparticles which generalize Majorana fermions and possess intriguing anyonic properties. The theoretical investigation of effective models hosting them is gaining considerable importance in view of present-day condensed-matter realizations where they have been predicted to appear. Here we study the simplest number-conserving model of particlelike Fock parafermions, namely a one-dimensional tight-binding model. By means of numerical simulations based on exact diagonalization and on the density-matrix renormalization group, we prove that this quadratic model is nonintegrable and displays bound states in the spectrum due to its peculiar anyonic properties. Moreover, we discuss its many-body physics, characterizing anyonic correlation functions and discussing the underlying Luttinger-liquid theory at low energies. In the case when Fock parafermions behave as fractionalized fermions, we are able to unveil interesting similarities with two counterpropagating edge modes of two neighboring Laughlin states at filling 1/3.

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

## Archive ouverte HAL – Anyons on the sphere: analytic states and spectrum

### Stephane Ouvry

^{1}Alexios P. Polychronakos#### Stephane Ouvry, Alexios P. Polychronakos. Anyons on the sphere: analytic states and spectrum.

*Nucl.Phys.B*, 2019, 949, pp.114797. ⟨10.1016/j.nuclphysb.2019.114797⟩. ⟨hal-02303026⟩We analyze the quantum mechanics of anyons on the sphere in the presence of a constant magnetic field. We introduce an operator method for diagonalizing the Hamiltonian and derive a set of exact anyon energy eigenstates, in partial correspondence with the known exact eigenstates on the plane. We also comment on possible connections of this system with integrable systems of the Calogero type.

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

## Archive ouverte HAL – Bulk organic aerosol analysis by PTR-MS: an improved methodology for the determination of total organic mass, O:C and H:C ele- mental ratios and the average molecular formula

### Joris Leglise

^{1}Markus Muller^{2}Felix Piel^{3}Tobias Otto^{4}Armin Wisthaler^{5, 6}#### Joris Leglise, Markus Muller, Felix Piel, Tobias Otto, Armin Wisthaler. Bulk organic aerosol analysis by PTR-MS: an improved methodology for the determination of total organic mass, O:C and H:C ele- mental ratios and the average molecular formula.

*Analytical Chemistry*, American Chemical Society, 2019, ⟨10.1021/acs.analchem.9b02949⟩. ⟨hal-02459530⟩We have recently shown in this journal (Müller et al., Anal. Chem. 2017, 89, 10889-10897) how a proton-transfer-reaction mass spectrometry (PTR-MS) analyzer measured particulate organic matter in urban atmospheres using the "Chemical Analysis of Aerosol Online" (CHARON) inlet. Our initial CHARON studies did not take into account fragmentation of protonated analyte molecules, which introduced a small but significant negative bias in the determination of bulk organic aerosol parameters. Herein, we studied the ionic fragmentation of 26 oxidized organic compounds typically found in atmospheric particles. This allowed us to derive a correction algorithm for the determination of the bulk organic mass concentration, m OA , the bulk-average hydrogen to carbon ratio, (H:C) bulk, the bulk-average oxygen-to-carbon, (O:C) bulk , and the bulk-average molecular formula, MF bulk. The correction algorithm was validated against AMS data using two sets of published data. Finally, we determined MF bulk of particles generated from the reaction of -pinene and ozone and compared and discussed the results in relation to the literature.

- 1. ICARE - Institut de Combustion, Aérothermique, Réactivité et Environnement
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IAU - Institute for Atmospheric and Environmental Sciences [Frankfurt/Main]
- 4. TROPOS - Leibniz Institute for Tropospheric Research
- 5. Institut für Ionenphysik und Angewandte Physik - Institute for Ion Physics and Applied Physics [Innsbruck]
- 6. UiO - University of Oslo

## Archive ouverte HAL – Can a periodically driven particle resist laser cooling and noise?

### A. Maitra

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1}#### A. Maitra, D. Leibfried, D. Ullmo, H. Landa. Can a periodically driven particle resist laser cooling and noise?.

*Physical Review Research*, American Physical Society, 2019, ⟨10.01856⟩. ⟨hal-02395528⟩Studying a single atomic ion confined in a time-dependent periodic anharmonic potential, we find large amplitude trajectories stable for millions of oscillation periods in the presence of stochastic laser cooling. The competition between energy gain from the time-dependent drive and damping leads to the stabilization of such stochastic limit cycles. Instead of converging to the global minimum of the averaged potential, the steady-state phase-space distribution develops multiple peaks in the regions of phase space where the frequency of the motion is close to a multiple of the periodic drive. Such distinct nonequilibrium behaviour can be observed in realistic radio-frequency traps with laser-cooled ions, suggesting that Paul traps offer a well-controlled test-bed for studying transport and dynamics of microscopically driven systems.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technology [Gaithersburg]

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

### Marco Baity-Jesi

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

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

## Archive ouverte HAL – Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems

### Ada Altieri

^{1}Silvio Franz^{2}*Physical Review E*, American Physical Society (APS), 2019, 99 (1), 〈10.1103/PhysRevE.99.010401〉We discuss a resource-competition model, which takes the MacArthur's model as a platform, to unveil interesting connections with glassy features and jamming in high dimension. This model presents two qualitatively different phases: a "shielded" phase, where a collective and self-sustained behavior emerges, and a "vulnerable" phase, where a small perturbation can destabilize the system and contribute to population extinction. We first present our perspective based on a strong similarity with continuous constraint satisfaction problems in their convex regime. Then, we discuss the stability in terms of the computation of the leading eigenvalue of the Hessian matrix of the free energy in the replica space. This computation allows us to efficiently distinguish between the two aforementioned phases and to relate high-dimensional critical ecosystems to glassy phenomena in the low-temperature regime.

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

## Archive ouverte HAL – Correlated Rigidity Percolation and Colloidal Gels

### Shang ZhangLeyou ZhangMehdi Bouzid

^{1, 2}D. Zeb RocklinEmanuela del Gado^{3}Xiaoming Mao^{4}#### Shang Zhang, Leyou Zhang, Mehdi Bouzid, D. Zeb Rocklin, Emanuela del Gado, et al.. Correlated Rigidity Percolation and Colloidal Gels.

*Physical Review Letters*, American Physical Society, 2019, 123 (5), ⟨10.1103/PhysRevLett.123.058001⟩. ⟨hal-02291872⟩Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.

- 1. PMMH - Physique et mécanique des milieux hétérogenes
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LCVN - Laboratoire des colloïdes, verres et nanomatériaux
- 4. UIUC - Physics Department

## Archive ouverte HAL – Critical Jammed Phase of the Linear Perceptron

### Silvio Franz

^{1}Antonio Sclocchi^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Critical Jammed Phase of the Linear Perceptron.

*Physical Review Letters*, American Physical Society, 2019, 123 (11), ⟨10.1103/PhysRevLett.123.115702⟩. ⟨hal-02292061⟩Criticality in statistical physics naturally emerges at isolated points in the phase diagram. Jamming of spheres is not an exception: varying density, it is the critical point that separates the unjammed phase where spheres do not overlap and the jammed phase where they cannot be arranged without overlaps. The same remains true in more general constraint satisfaction problems with continuous variables (CCSP) where jamming coincides with the (protocol dependent) satisfiability transition point. In this work we show that by carefully choosing the cost function to be minimized, the region of criticality extends to occupy a whole region of the jammed phase. As a working example, we consider the spherical perceptron with a linear cost function in the unsatisfiable (UNSAT) jammed phase and we perform numerical simulations which show critical power laws emerging in the configurations obtained minimizing the linear cost function. We develop a scaling theory to compute the emerging critical exponents.

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

## Archive ouverte HAL – Darcy’s Law for Yield Stress Fluids

### Chen Liu

^{1}Andrea de Luca^{2}Alberto Rosso^{3}Laurent Talon^{1}#### Chen Liu, Andrea de Luca, Alberto Rosso, Laurent Talon. Darcy’s Law for Yield Stress Fluids.

*Physical Review Letters*, American Physical Society, 2019, 122 (24), ⟨10.1103/PhysRevLett.122.245502⟩. ⟨hal-02165315⟩- 1. FAST - Fluides, automatique, systèmes thermiques
- 2. Rudolf Peierls Center for Theoretical Physics
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Distribution of Brownian coincidences

### Alexandre Krajenbrink

^{1}Bertrand Lacroix-A-Chez-Toine^{2}Pierre Le Doussal^{3}#### Alexandre Krajenbrink, Bertrand Lacroix-A-Chez-Toine, Pierre Le Doussal. Distribution of Brownian coincidences.

*Journal of Statistical Physics*, Springer Verlag, 2019. ⟨hal-02295902⟩We study the probability distribution, $P_N(T)$, of the coincidence time $T$, i.e. the total local time of all pairwise coincidences of $N$ independent Brownian walkers. We consider in details two geometries: Brownian motions all starting from $0$, and Brownian bridges. Using a Feynman-Kac representation for the moment generating function of this coincidence time, we map this problem onto some observables in three related models (i) the propagator of the Lieb Liniger model of quantum particles with pairwise delta function interactions (ii) the moments of the partition function of a directed polymer in a random medium (iii) the exponential moments of the solution of the Kardar-Parisi-Zhang equation. Using these mappings, we obtain closed formulae for the probability distribution of the coincidence time, its tails and some of its moments. Its asymptotics at large and small coincidence time are also obtained for arbitrary fixed endpoints. The universal large $T$ tail, $P_N(T) \sim \exp(- 3 T^2/(N^3-N))$ is obtained, and is independent of the geometry. We investigate the large deviations in the limit of a large number of walkers through a Coulomb gas approach. Some of our analytical results are compared with numerical simulations.

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

## Archive ouverte HAL – Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

### Grégoire Misguich

^{1}Nicolas Pavloff^{2}Vincent Pasquier^{1}#### Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier. Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point.

*SciPost Physics*, SciPost Foundation, 2019, 7 (2), ⟨10.21468/SciPostPhys.7.2.025⟩. ⟨hal-02295825⟩We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.

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

## Archive ouverte HAL – Electric double layers with surface charge modulations: Novel exact Poisson-Boltzmann solutions

### L. Samaj

^{1}E. Trizac^{2}#### L. Samaj, E. Trizac. Electric double layers with surface charge modulations: Novel exact Poisson-Boltzmann solutions.

*Physical Review E*, American Physical Society (APS), 2019, ⟨10.02870⟩. ⟨hal-02421677⟩Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide novel exact analytical solutions to this non-linear mean-field approach, for the diffuse layer of ions in the vicinity of a planar or a cylindrical macroion. While previously known solution are for homogeneously charged objects, the cases worked out exhibit a modulated surface charge --or equivalently surface potential-- on the macroion (wall) surface. In addition to asymptotic features at large distances from the wall, attention is paid to the fate of the contact theorem, relating the contact density of ions to the local wall charge density. For salt-free systems (counterions only), we make use of results pertaining to the two-dimensional Liouville equation, supplemented by an inverse approach. When salt is present, we invoke the exact two-soliton solution to the 2D sinh-Gordon equation. This leads to inhomogeneous charge patterns, that are either localized or periodic in space. Without salt, the electrostatic signature of a charge pattern on the macroion fades exponentially with distance for a planar macroion, while it decays as an inverse power-law for a cylindrical macroion. With salt, our study is limited to the planar geometry, and reveals that pattern screening is exponential.

- 1. INSTITUTE OF PHYSICS - SLOVAK ACADEMY OF SCIENCES Institute of Physics Dubraska cesta 9, 84228 Bratislava, Slovaquie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Electromagnetic surface wave propagation in a metallic wire and the Lambert W function

### J. Ricardo G. Mendonça

^{1}#### J. Ricardo G. Mendonça. Electromagnetic surface wave propagation in a metallic wire and the Lambert W function.

*American Journal of Physics*, American Association of Physics Teachers, 2019, 87 (6), pp.476-484. ⟨10.1119/1.5100943⟩. ⟨hal-02291821⟩We revisit the solution due to Sommerfeld of a problem in classical electrodynamics, namely, that of the propagation of an electromagnetic axially symmetric surface wave (a low-attenuation single TM$_{01}$ mode) in a cylindrical metallic wire, and his iterative method to solve the transcendental equation that appears in the determination of the propagation wave number from the boundary conditions. We present an elementary analysis of the convergence of Sommerfeld's iterative solution of the approximate problem and compare it with both the numerical solution of the exact transcendental equation and the solution of the approximate problem by means of the Lambert $W$ function.

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

## Archive ouverte HAL – Electrophoresis of active Janus particles

### Parvin Bayati

^{1}Ali Najafi#### Parvin Bayati, Ali Najafi. Electrophoresis of active Janus particles.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 150 (23), pp.234902. ⟨10.1063/1.5101023⟩. ⟨hal-02291804⟩We theoretically consider the dynamics of a self-propelled active Janus motor moving in an external electric field. The external field can manipulate the route of a Janus particle and enforce it to move towards the desired targets. To investigate the trajectory of this active motor, we use a perturbative scheme. At the leading orders of surface activity of the Janus particle and also the external field, the orientational dynamics of the Janus particles behave like a mathematical pendulum with an angular the velocity that is sensitive to both the electric field and surface activity of the motor.

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

## Archive ouverte HAL – Enhancement of many-body quantum interference in chaotic bosonic systems

### Peter Schlagheck

^{1}Denis Ullmo^{2}Juan Diego Urbina^{3}Klaus RichterSteven Tomsovic^{4}#### Peter Schlagheck, Denis Ullmo, Juan Diego Urbina, Klaus Richter, Steven Tomsovic. Enhancement of many-body quantum interference in chaotic bosonic systems.

*Physical Review Letters*, American Physical Society, 2019, 123, pp.215302. ⟨10.1103/PhysRevLett.123.215302⟩. ⟨hal-02361335⟩Although highly successful, the truncated Wigner approximation (TWA) leaves out many-body quantum interference between mean-field Gross-Pitaevskii solutions as well as other quantum effects, and is therefore essentially classical. Turned around, this implies that if a system's quantum properties deviate from TWA, they must be exhibiting some quantum phenomenon, such as localization, diffraction, or tunneling. Here, we consider in detail a particular interference effect arising from discrete symmetries, which can lead to a significant enhancement of quantum observables with respect to the TWA prediction, and derive an augmented version of the TWA in order to incorporate them. Using the Bose-Hubbard model for illustration, we further show strong evidence for the presence of dynamical localization due to remaining differences between the TWA predictions and quantum results.

- 1. Institut für Theoretische Physik
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. UR - Universität Regensburg
- 4. Department of Physics

## Archive ouverte HAL – Exactly Solvable Record Model for Rainfall

### Satya N. Majumdar

^{1}Philipp von BomhardJoachim Krug^{2}Satya Majumdar^{1}#### Satya N. Majumdar, Philipp von Bomhard, Joachim Krug, Satya Majumdar. Exactly Solvable Record Model for Rainfall.

*Physical Review Letters*, American Physical Society, 2019, 122 (15), ⟨10.1103/PhysRevLett.122.158702⟩. ⟨hal-02291862⟩Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability $p$, we show that the presence of dry days induces negative correlations between record-breaking precipitation events. The resulting non-monotonic behavior of the Fano factor of the record counting process is recovered in empirical data. We derive the full probability distribution $P(R,n)$ of the number of records $R_n$ up to time $n$, and show that for large $n$, its large deviation form coincides with that of a Poisson distribution with parameter $\ln(p\,n)$. We also study in detail the joint limit $p \to 0$, $n \to \infty$, which yields a random record model in continuous time $t = pn$.

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

## Archive ouverte HAL – Exclusion Statistics and lattice random walks

### Stéphane Ouvry

^{1}Alexios Polychronakos^{2}#### Stéphane Ouvry, Alexios Polychronakos. Exclusion Statistics and lattice random walks.

*Nuclear Physics B*, Elsevier, 2019, 949, pp.114797. ⟨10.1016/j.nuclphysb.2019.114731⟩. ⟨hal-02409911⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Physics Department

## Archive ouverte HAL – Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

### A. Maitra

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1}#### A. Maitra, D. Leibfried, D. Ullmo, H. Landa. Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps.

*Physical Review A*, American Physical Society 2019, 99 (4), ⟨10.1103/PhysRevA.99.043421⟩. ⟨hal-02291892⟩We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technology [Gaithersburg]

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

### Eugenio LippielloGiuseppe PetrilloFrançois Landes

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

*Bulletin of the Seismological Society of America*, Seismological Society of America, 2019, 109 (3), pp.1156-1163. ⟨10.1785/0120180244⟩. ⟨hal-02156407⟩- 1. LRI - Laboratoire de Recherche en Informatique
- 2. TAU - TAckling the Underspecified
- 3. UP11 UFR Sciences - Université Paris-Sud 11 - Faculté des Sciences
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Fermi surface enlargement on the Kondo lattice

### Eoin Quinn

^{1}Onur Erten#### Eoin Quinn, Onur Erten. Fermi surface enlargement on the Kondo lattice.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 99 (24), ⟨10.1103/PhysRevB.99.245123⟩. ⟨hal-02291818⟩The Kondo lattice model is a paradigmatic model for the description of local moment systems, a class of materials exhibiting a range of strongly correlated phenomena including heavy fermion formation, magnetism, quantum criticality and unconventional superconductivity. Conventional theoretical approaches invoke fractionalization of the local moment spin through large-N and slave particle methods. In this work we develop a new formalism, based instead on non-canonical degrees of freedom. We demonstrate that the graded Lie algebra su(2|2) provides a powerful means of organizing correlations on the Kondo lattice through a splitting of the electronic degree of freedom, in a manner which entwines the conduction electrons with the local moment spins. This offers a novel perspective on heavy fermion formation. Unlike slave-particle methods, non-canonical degrees of freedom generically allow for a violation of the Luttinger sum rule, and we interpret recent angle resolved photoemission experiments on Ce-115 systems in view of this.

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

## Archive ouverte HAL – Fiber plucking by molecular motors yields large emergent contractility in stiff biopolymer networks

### Pierre Ronceray

^{1}Chase P. Broedersz^{2}Martin Lenz^{3, 4}*Soft Matter*, Royal Society of Chemistry, 2019The mechanical properties of the cell depend crucially on the tension of its cytoskeleton, a biopolymer network that is put under stress by active motor proteins. While the fibrous nature of the network is known to strongly affect the transmission of these forces to the cellular scale, our understanding of this process remains incomplete. Here we investigate the transmission of forces through the network at the individual filament level, and show that active forces can be geometrically amplified as a transverse motor-generated force force "plucks" the fiber and induces a nonlinear tension. In stiff and densely connnected networks, this tension results in large network-wide tensile stresses that far exceed the expectation drawn from a linear elastic theory. This amplification mechanism competes with a recently characterized network-level amplification due to fiber buckling, suggesting that that fiber networks provide several distinct pathways for living systems to amplify their molecular forces.

- 1. Princeton Center for Theoretical Science
- 2. LMU - Ludwig-Maximilians-Universität München
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment

## Archive ouverte HAL – Fluctuation-dominated phase ordering at a mixed order transition

### Mustansir Barma

^{1}Satya N. Majumdar^{2}David Mukamel^{3}Satya Majumdar^{2}#### Mustansir Barma, Satya N. Majumdar, David Mukamel, Satya Majumdar. Fluctuation-dominated phase ordering at a mixed order transition.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (25), pp.254001. ⟨10.1088/1751-8121/ab2064⟩. ⟨hal-02291900⟩Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.

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

## Archive ouverte HAL – Free energy of cylindrical polyions: Analytical results

### Emmanuel Trizac

^{1}Gabriel Tellez^{2}#### Emmanuel Trizac, Gabriel Tellez. Free energy of cylindrical polyions: Analytical results.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 151 (12), pp.124904. ⟨10.1063/1.5121724⟩. ⟨hal-02395512⟩Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged soft matter problems, we work out the Coulombic grand potential of a long cylindrical charged polyion in a binary electrolyte solution of arbitrary valency and for low salt concentration. We obtain the exact analytical low-salt asymptotic expression for the grand potential, derived from known properties of the exact solutions to the cylindrical PB equation. These results are relevant for understanding nucleic acid processes. In practice, our expressions are accurate for arbitrary polyion charges, provided their radius is smaller than the Debye length defined by the electrolyte.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departamento de Fisica

## Archive ouverte HAL – Free fermions and α -determinantal processes

### Fabio Deelan Cunden

^{1}Satya N. Majumdar^{2}Neil O'Connell^{1}#### Fabio Deelan Cunden, Satya N. Majumdar, Neil O'Connell. Free fermions and α -determinantal processes.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (16), pp.165202. ⟨10.1088/1751-8121/ab0ebd⟩. ⟨hal-02102134⟩The $\alpha$-determinant is a one-parameter generalisation of the standard determinant, with $\alpha=-1$ corresponding to the determinant, and $\alpha=1$ corresponding to the permanent. In this paper a simple limit procedure to construct $\alpha$-determinantal point processes out of fermionic processes is examined. The procedure is illustrated for a model of $N$ free fermions in a harmonic potential. When the system is in the ground state, the rescaled correlation functions converge for large $N$ to determinants (of the sine kernel in the bulk and the Airy kernel at the edges). We analyse the point processes associated to a special family of excited states of fermions and show that appropriate scaling limits generate $\alpha$-determinantal processes. Links with wave optics and other random matrix models are suggested.

- 1. UCD - University College Dublin [Dublin]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – From chiral anomaly to two-fluid hydrodynamics for electronic vortices

### S. Brazovskii

^{1}N. Kirova^{2}*Annals Phys.*, 2019, 403, pp.184-197. 〈10.1016/j.aop.2018.07.004〉Many recent experiments addressed manifestations of electronic crystals, particularly the charge density waves, in nano-junctions, under electric field effect, at high magnetic fields, together with real space visualizations by STM and micro X-ray diffraction. This activity returns the interest to stationary or transient states with static and dynamic topologically nontrivial configurations: electronic vortices as dislocations, instantons as phase slip centers, and ensembles of microscopic solitons. Describing and modeling these states and processes calls for an efficient phenomenological theory which should take into account the degenerate order parameter, various kinds of normal carriers and the electric field. Here we notice that the commonly employed time-depend Ginzburg–Landau approach suffers with violation of the charge conservation law resulting in unphysical generation of particles which is particularly strong for nucleating or moving electronic vortices. We present a consistent theory which exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The resulting equations clarify partitions of charges, currents and rigidity among subsystems of the condensate and normal carriers. On this basis we perform the numerical modeling of a spontaneously generated coherent sequence of phase slips – the spacetime vortices – serving for the conversion among the injected normal current and the collective one.

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

## Archive ouverte HAL – Gap statistics close to the quantile of a random walk

### Bertrand Lacroix-A-Chez-Toine

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}Satya Majumdar^{1}#### Bertrand Lacroix-A-Chez-Toine, Satya N. Majumdar, Gregory Schehr, Satya Majumdar. Gap statistics close to the quantile of a random walk.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (31), pp.315003. ⟨10.1088/1751-8121/ab2cf9⟩. ⟨hal-02291855⟩We consider a random walk of $n$ steps starting at $x_0=0$ with a double exponential (Laplace) jump distribution. We compute exactly the distribution $p_{k,n}(\Delta)$ of the gap $d_{k,n}$ between the $k^{\rm th}$ and $(k+1)^{\rm th}$ maxima in the limit of large $n$ and large $k$, with $\alpha=k/n$ fixed. We show that the typical fluctuations of the gaps, which are of order $O( n^{-1/2})$, are described by a universal $\alpha$-dependent distribution, which we compute explicitly. Interestingly, this distribution has an inverse cubic tail, which implies a non-trivial $n$-dependence of the moments of the gaps. We also argue, based on numerical simulations, that this distribution is universal, i.e. it holds for more general jump distributions (not only the Laplace distribution), which are continuous, symmetric with a well defined second moment. Finally, we also compute the large deviation form of the gap distribution $p_{\alpha n,n}(\Delta)$ for $\Delta=O(1)$, which turns out to be non-universal.

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

## Archive ouverte HAL – Harmonically Confined Particles with Long-Range Repulsive Interactions

### Sanaa AgarwalAbhishek Dhar

^{1}Manas KulkarniAnupam Kundu^{1}Satya N. Majumdar^{2}David Mukamel^{3}Gregory Schehr^{2}S. n. Majumdar#### Sanaa Agarwal, Abhishek Dhar, Manas Kulkarni, Anupam Kundu, Satya N. Majumdar, et al.. Harmonically Confined Particles with Long-Range Repulsive Interactions.

*Physical Review Letters*, American Physical Society, 2019, 123 (10), ⟨10.1103/PhysRevLett.123.100603⟩. ⟨hal-02295905⟩We study an interacting system of $N$ classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law $\propto \sum_{\substack{i\neq j}}^N|x_i-x_j|^{-k}$ (with $k>-2$) of their mutual distance. This is a generalization of the well known cases of the one component plasma ($k=-1$), Dyson's log-gas ($k\to 0^+$), and the Calogero-Moser model ($k=2$). Due to the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all $k>-2$. We compute exactly the average density profile for large $N$ for all $k>-2$ and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on $k$ with distinct behavior for $-2

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

## Archive ouverte HAL – High-temperature expansions and message passing algorithms

### Antoine Maillard

^{1, *}Laura Foini^{2}Alejandro Lage Castellanos^{3}Florent Krzakala^{1}Marc Mezard^{4}Lenka Zdeborová^{2}#### Antoine Maillard, Laura Foini, Alejandro Lage Castellanos, Florent Krzakala, Marc Mezard, et al.. High-temperature expansions and message passing algorithms.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (11), pp.113301. ⟨10.1088/1742-5468/ab4bbb⟩. ⟨cea-02524865⟩Improved mean-eld technics are a central theme of statistical physics methods applied to inference and learning. We revisit here some of these methods using high-temperature expansions for disordered systems initiated by Plefka, Georges and Yedidia. We derive the Gibbs free entropy and the subsequent self-consistent equations for a generic class of statistical models with correlated matrices and show in particular that many classical approximation schemes, such as adaptive TAP, Expectation-Consistency, or the approximations behind the Vector Approximate Message Passing algorithm all rely on the same assumptions, that are also at the heart of high-temperature expansions. We focus on the case of rotationally invariant random coupling matrices in the 'high-dimensional' limit in which the number of samples and the dimension are both large, but with a xed ratio. This encapsulates many widely studied models, such as Restricted Boltzmann Machines or Generalized Linear Models with correlated data matrices. In this general setting, we show that all the approximation schemes described before are equivalent, and we conjecture that they are exact in the thermodynamic limit in the replica symmetric phases. We achieve this conclusion by resummation of the in nite perturbation series, which generalises a seminal result of Parisi and Potters. A rigorous derivation of this conjecture is an interesting mathematical challenge. On the way to these conclusions, we uncover several diagrammatical results in connection with free probability and random matrix theory, that are interesting independently of the rest of our work.

- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 3. University of Havana - Departamento de Física Teórica
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – How collective asperity detachments nucleate slip at frictional interfaces

### Tom W. J. de GeusMarko Popović

^{1}Wencheng JiAlberto Rosso^{2}Matthieu Wyart^{3}#### Tom W. J. de Geus, Marko Popović, Wencheng Ji, Alberto Rosso, Matthieu Wyart. How collective asperity detachments nucleate slip at frictional interfaces.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2019. ⟨hal-02395574⟩Sliding at a quasi-statically loaded frictional interface occurs via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_\sigma$ presents a pseudo-gap $P(x_\sigma) \sim (x_\sigma)^\theta$, where $\theta$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $\theta$-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

- 1. MPI-PKS - Max Planck Institute for the Physics of Complex Systems
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. EPFL - Ecole Polytechnique Fédérale de Lausanne

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

### Thierry Mora

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

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

## Archive ouverte HAL – Impact of jamming criticality on low-temperature anomalies in structural glasses

### Silvio Franz

^{1}Thibaud Maimbourg^{2, 1}Giorgio Parisi^{3}Antonello Scardicchio^{4}#### Silvio Franz, Thibaud Maimbourg, Giorgio Parisi, Antonello Scardicchio. Impact of jamming criticality on low-temperature anomalies in structural glasses.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2019, 116 (28), pp.13768-13773. ⟨10.1073/pnas.1820360116⟩. ⟨hal-02292219⟩We present a novel mechanism for the anomalous behaviour of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a crossover temperature above which the specific heat scales linearly with temperature while below it a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) The marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling (ii) The vicinity of the classical jamming critical point, as the crossover temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals, the Debye approximation does not hold.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica
- 4. ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]

## Archive ouverte HAL – Intermediate deviation regime for the full eigenvalue statistics in the complex Ginibre ensemble

### Bertrand Lacroix-A-Chez-Toine

^{1}Jeyson Andres Monroy GarzonChristopher Sebastian Hidalgo CalvaAnupam Kundu^{2}Satya N. Majumdar^{1}Jeyson Andrés Monroy GarzónIsaac Pérez Castillo^{3}Satya Majumdar^{1}Gregory Schehr^{1}#### Bertrand Lacroix-A-Chez-Toine, Jeyson Andres Monroy Garzon, Christopher Sebastian Hidalgo Calva, Anupam Kundu, Satya N. Majumdar, et al.. Intermediate deviation regime for the full eigenvalue statistics in the complex Ginibre ensemble.

*Physical Review E*, American Physical Society (APS), 2019, 100 (1), ⟨10.1103/PhysRevE.100.012137⟩. ⟨hal-02291786⟩We study the Ginibre ensemble of $N \times N$ complex random matrices and compute exactly, for any finite $N$, the full distribution as well as all the cumulants of the number $N_r$ of eigenvalues within a disk of radius $r$ centered at the origin. In the limit of large $N$, when the average density of eigenvalues becomes uniform over the unit disk, we show that for $0

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 3. Departamento de Sistemas Complejos, Instituto de Física, UNAM

## Archive ouverte HAL – Intertwined chiral charge orders and topological stabilization of the light-induced state of a prototypical transition metal dichalcogenide

### Yaroslav A. GerasimenkoPeter KarpovIgor Vaskivskyi

^{1}Serguei Brazovskii^{2}Dragan Mihailovic^{3}Yaroslav GerasimenkoPetr Karpov^{4}#### Yaroslav A. Gerasimenko, Peter Karpov, Igor Vaskivskyi, Serguei Brazovskii, Dragan Mihailovic, et al.. Intertwined chiral charge orders and topological stabilization of the light-induced state of a prototypical transition metal dichalcogenide.

*NPJ QUANTUM MATERIALS*, 2019, 4 (1), ⟨10.1038/s41535-019-0172-1⟩. ⟨hal-02421684⟩The fundamental idea that the constituents of interacting many body systems in complex quantum materials may self-organise into long range order under highly non-equilibrium conditions leads to the notion that entirely new and unexpected functionalities might be artificially created. However, demonstrating new emergent order in highly non-equilibrium transitions has proven surprisingly difficult. In spite of huge recent advances in experimental ultrafast time-resolved techniques, methods that average over successive transition outcomes have so far proved incapable of elucidating the emerging spatial structure. Here, using scanning tunneling microscopy, we report for the first time the charge order emerging after a single transition outcome in a prototypical two-dimensional dichalcogenide 1T-TaS$_2$ initiated by a single optical pulse. By mapping the vector field of charge displacements of the emergent state, we find surprisingly intricate, long-range, topologically non-trivial charge order in which chiral domain tiling is intertwined with unique unpaired dislocations which play a crucial role in enhancing the emergent states remarkable stability. The discovery of the principles that lead to metastability in charge-ordered systems open the way to designing novel emergent functionalities, particularly ultrafast all-electronic non-volatile cryo-memories.

- 1. University of Ljubljana
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. CENN Nanocenter
- 4. MISIS - National University of Science and Technology

## Archive ouverte HAL – Jamming in Multilayer Supervised Learning Models

### Silvio Franz

^{1}Sungmin Hwang^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Sungmin Hwang, Pierfrancesco Urbani. Jamming in Multilayer Supervised Learning Models.

*Physical Review Letters*, American Physical Society, 2019, 123 (16), ⟨10.1103/PhysRevLett.123.160602⟩. ⟨hal-02395521⟩Critical jamming transitions are characterized by an astonishing degree of universality. Analytic and numerical evidence points to the existence of a large universality class that encompasses finite and infinite dimensional spheres and continuous constraint satisfaction problems (CCSP) such as the non-convex perceptron and related models. In this paper we investigate multilayer neural networks (MLNN) learning random associations as models for CCSP which could potentially define different jamming universality classes. As opposed to simple perceptrons and infinite dimensional spheres, which are described by a single effective field in terms of which the constraints appear to be one-dimensional, the description of MLNN, involves multiple fields, and the constraints acquire a multidimensional character. We first study the models numerically and show that similarly to the perceptron, whenever jamming is isostatic, the sphere universality class is recovered, we then write the exact mean-field equations for the models and identify a dimensional reduction mechanism that leads to a scaling regime identical to one of the infinite dimensional spheres. We suggest that this mechanism could be general enough to explain finite dimensional universality.

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

## Archive ouverte HAL – Lattice Boltzmann Electrokinetics simulation of nanocapacitors

### Adelchi J. Asta

^{1}Ivan Palaia^{2}Emmanuel Trizac^{2}Maximilien Levesque^{3}Benjamin Rotenberg^{4}#### Adelchi J. Asta, Ivan Palaia, Emmanuel Trizac, Maximilien Levesque, Benjamin Rotenberg. Lattice Boltzmann Electrokinetics simulation of nanocapacitors.

*Journal of Chemical Physics*, American Institute of Physics, 2019. ⟨hal-02295839⟩We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics simulations (LBE), a lattice-based algorithm rooted in kinetic theory which captures the coupled solvent and ion dynamics in electrolyte solutions. This is achieved by a simple rule to impose electrostatic boundary conditions, in a consistent way with the location of the hydrodynamic interface for stick boundary conditions. The proposed method also provides the local charge induced on the electrode by the instantaneous distribution of ions under voltage. We validate it in the low voltage regime by comparison with analytical results in two model nanocapacitors: parallel plate and coaxial electrodes. We examine the steady-state ionic concentrations and electric potential profiles (and corresponding capacitance), the time-dependent response of the charge on the electrodes, as well as the steady-state electro-osmotic profiles in the presence of an additional, tangential electric field. The LBE method further provides the time-dependence of these quantities, as illustrated on the electro-osmotic response. While we do not consider this case in the present work, which focuses on the validation of the method, the latter readily applies to large voltages between the electrodes, as well as to time-dependent voltages. This work opens the way to the LBE simulation of more complex systems involving electrodes and metallic surfaces, such as sensing devices based on nanofluidic channels and nanotubes, or porous electrodes.

- 1. PHENIX - PHysicochimie des Electrolytes et Nanosystèmes InterfaciauX
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PASTEUR - Processus d'Activation Sélective par Transfert d'Energie Uni-électronique ou Radiatif (UMR 8640)
- 4. PECSA - Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques

## Archive ouverte HAL – Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method

### M. Isoard

^{1}A. M. Kamchatnov^{2}N. Pavloff^{1}*Physical Review E*, American Physical Society (APS), 2019, 〈10.07952〉We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton, but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.

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

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

### Urna Basu

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

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

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

## Archive ouverte HAL – Many-body localization in continuum systems: Two-dimensional bosons

### G. Bertoli

^{1}B. L. Altshuler^{2}G. V. Shlyapnikov^{1}#### G. Bertoli, B. L. Altshuler, G. V. Shlyapnikov. Many-body localization in continuum systems: Two-dimensional bosons.

*Physical Review A*, American Physical Society 2019, 100 (1), ⟨10.1103/PhysRevA.100.013628⟩. ⟨hal-02291788⟩We demonstrate that many-body localization of two-dimensional weakly interacting bosons in disorder remains stable in the thermodynamic limit at sufficiently low temperatures. Highly energetic particles destroy the localized state only above a critical temperature, which increases with the strength of the disorder. If the particle distribution is truncated at high energies, as it does for cold atom systems, the localization can be stable at any temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Physics Dept.

## Archive ouverte HAL – Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation

### Thibault Bonnemain

^{1, 2}Denis Ullmo^{1}#### Thibault Bonnemain, Denis Ullmo. Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation.

*Physica A: Statistical Mechanics and its Applications*, Elsevier, 2019, 523, pp.310-325. ⟨10.1016/j.physa.2019.01.143⟩. ⟨hal-02102129⟩Motivated by the study of a Mean Field Game toy model called the "seminar problem", we consider the Fokker-Planck equation in the small noise regime for a specific drift field. This gives us the opportunity to discuss the application to diffusion problem of the WKB approach "a la Maslov", making it possible to solve directly the time dependant problem in an especially transparent way.

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

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

### M. Mert Terzi

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

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

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

### Christophe Gardella

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

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

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

### S. Brazovskii

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

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

## Archive ouverte HAL – Multifractality of open quantum systems

### Agustín M. Bilen

^{1}Ignacio García-Mata^{1}Bertrand Georgeot^{2}Olivier Giraud^{3}#### Agustín M. Bilen, Ignacio García-Mata, Bertrand Georgeot, Olivier Giraud. Multifractality of open quantum systems.

*Physical Review E*, American Physical Society (APS), 2019, 100, pp.032223. ⟨10.1103/PhysRevE.100.032223⟩. ⟨hal-02156304⟩We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and we quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but these states are multifractal instead of ergodic at each level of the hierarchy. This is visible for sufficiently long-lived resonance states at scales smaller than the classical structures. Our results can guide experimentalists in order to observe multifractal behavior in open systems.

- 1. IFIMAR - Instituto de Investigaciones Físicas de Mar del Plata
- 2. Information et Chaos Quantiques (LPT)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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

### Valerio Astuti

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

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

- 1. Dipartimento di Fisica, Università “La Sapienza"
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica

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

### Pierre Le Doussal

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

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

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

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

### David S. Dean

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

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

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

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

### David S. Dean

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

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

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

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

### Marco Picco

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

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

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

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

### Sungmin Hwang

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

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

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

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

### Maurizio Fagotti

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

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

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

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

### X. DengS. RayS. Sinha

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

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

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

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

### D. V. Kurlov

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

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

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

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

### N. Milazzo

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

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

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

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

### Carlos A. Plata

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

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

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

### Elisabeth Agoritsas

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

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

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

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

### P. Karpov

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

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

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

### Matthias BerweinNora Brambilla

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

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

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

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

### Frank Den Hollander

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

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

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

## Archive ouverte HAL – Quadratic Mean Field Games

### Denis Ullmo

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

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

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

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

### Thierry Jolicoeur

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

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

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

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

### Martín Carballo-PachecoJonathan Desponds

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

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

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

### Vladimir BelavinYoshishige HaraokaRaoul Santachiara

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

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

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

### Nadia Milazzo

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

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

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

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

### Tirthankar Banerjee

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

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

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

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

### Bertrand Lacroix-A-Chez-Toine

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

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

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

### Abhishek Dhar

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

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

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

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

### Jonathan Bares

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

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

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

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

### Stéphane Faure

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

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

### J. Ricardo G. Mendonça

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

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

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

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

### Satya Majumdar

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

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

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

### Ananyo Maitra

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

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

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

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

### Tirthankar Banerjee

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

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

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

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

### Pierre Ronceray

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

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

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

### Stephane Ouvry

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

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

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

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

### Enej IlievskiEoin Quinn

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

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

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

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

### A. Pricoupenko

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

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

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

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

### Francesco Mori

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

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

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

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

### Peng Cheng

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

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

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

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

### Anis Senoussi

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

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

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

### Alexander GorskyAlexey MilekhinSergei Nechaev

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

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

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

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

### M. Isoard

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

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

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

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

### Satya Majumdar

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

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

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

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

### Marco Baity-Jesi

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

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

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

### Eugenio Lippiello

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

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

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

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

### Thierry Mora

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

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

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

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

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

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

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

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

### Urna Basu

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

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

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

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

### M. Mert Terzi

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

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

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

### Christophe Gardella

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

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

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

### S. Brazovskii

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

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

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

### Martín Carballo-PachecoJonathan Desponds

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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