# LPTMS Publications

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## Absolutely classical spin states

### F. Bohnet-Waldraff

^{1, 2}O. Giraud^{1}D. Braun^{2}*Physical Review A*, American Physical Society, 2017, 95 (1), pp.012318We introduce the concept of "absolutely classical" spin states, in analogy to absolutely separable states of bi-partite quantum systems. Absolutely classical states are states that remain classical under any unitary transformation applied to them. We investigate the maximum ball of absolutely classical states centered on the fully mixed state that can be inscribed into the set of classical states, and derive a lower bound for its radius as function of the total spin quantum number. The result is compared to the case of absolutely separable states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Eberhard Karls Universität Tübingen

## Analysis of coherent quantum cryptography protocol vulnerability to an active beam-splitting attack

### A K KronbergE. O. Kiktenko

^{1}A. K. Fedorov^{2}Y. V. Kurochkin^{3}D. A. Kronberg*Quantum Electronics*, Turpion, 2017, 47 (2), pp.163 - 168We consider a new type of attack on a coherent quantum key distribution protocol [coherent one-way (COW) protocol]. The main idea of the attack consists in measuring individually the intercepted states and sending the rest of them unchanged. We have calculated the optimum values of the attack parameters for an arbitrary length of a channel length and compared this novel attack with a standard beam-splitting attack.

- 1. Bauman Moscow State Technical University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Russian Quantum Center

## Asymptotically optimal control for a simplest distributed system

### Alexander Ovseevich

^{1}Aleksey Fedorov^{2}*Доклады Академии Наук / Doklady Mathematics*, MAIK Nauka/Interperiodica, 2017, 95 (2), pp.194 - 197We study the problem of the minimum-time damping of a closed string under a bounded load, applied at a single fixed point. A constructive feedback control law is designed, which allows bringing the system to a bounded neighbourhood of the terminal manifold. The law has the form of the dry friction at the point, where the load is applied. The motion under the control is governed by a nonlinear wave equation. The existence and uniqueness of solution of the Cauchy problem for this equation are proved. The main result is the asymptotic optimality of the suggested control law.

- 1. Institute for Problems in Mechanics of Russian Academy of Sciences
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Bloch oscillations in the absence of a lattice

### Florian Meinert

^{1}Michael Knap^{2}Emil Kirilov^{1}Katharina Jag-Lauber^{1}Mikhail B. Zvonarev^{3}Eugene Demler^{4}Hanns-Christoph Nägerl^{1}*Science*, American Association for the Advancement of Science, 2017, 356 (6341), pp.945 - 948We experimentally investigate the quantum motion of an impurity atom that is immersed in a strongly interacting one-dimensional Bose liquid and is subject to an external force. We find that the momentum distribution of the impurity exhibits characteristic Bragg reflections at the edge of an emergent Brillouin zone. While Bragg reflections are typically associated with lattice structures, in our strongly correlated quantum liquid they result from the interplay of short-range crystalline order and kinematic constraints on the many-body scattering processes in the one-dimensional system. As a consequence, the impurity exhibits periodic dynamics that we interpret as Bloch oscillations, which arise even though the quantum liquid is translationally invariant. Our observations are supported by large-scale numerical simulations.

- 1. Institut für Experimentalphysik und Zentrum für Quantenphysik Universitat Innsbruck
- 2. TUM - Technical University of Munich
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Harvard University [Cambridge]

## Cleaning large correlation matrices: tools from random matrix theory

### Joël Bun

^{1, 2}Jean-Philippe Bouchaud^{2}Marc Potters^{2}*Physics Reports*, Elsevier, 2017, 666, pp.1This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CFM - Capital Fund Management

## Conditioned random walks and interaction-driven condensation

### Juraj Szavits-Nossan

^{1}Martin R. Evans^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2017, 50 (2), pp.024005We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having area $a$ and returning to the origin for the first time after time $\tau$. We then show how condensation occurs when the total area constraint is increased: an excursion containing a finite fraction of the area emerges. Finally we show how the phenomena generalises previously studied cases of condensation induced by several constraints and how it is related to interaction-driven condensation which allows us to explain the phenomenon in the framework of large deviation theory.

- 1. SUPA, School of Physics, University of Edinburgh
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Configurational and energy landscape in one-dimensional Coulomb systems

### Lucas Varela

^{1}Gabriel Téllez^{1}Emmanuel Trizac^{2}*Physical Review E*, American Physical Society (APS), 2017, 95 (2), pp.022112We study a one dimensional Coulomb system, where two charged colloids are neutralized by a collection of point counterions, with global neutrality. Temperature being given, two situations are addressed: the colloids are either kept at fixed positions (canonical ensemble), or the force acting on the colloids is fixed (isobaric-isothermal ensemble). The corresponding partition functions are worked out exactly, in view of determining which arrangement of counterions is optimal: how many counterions should be in the confined segment between the colloids? For the remaining ions outside, is there a left/right symmetry breakdown? We evidence a cascade of transitions, as system size is varied in the canonical treatment, or as pressure is increased in the isobaric formulation.

- 1. Universidad de los Andes
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions

### Jerome Dubail

^{1}Raoul Santachiara^{2}Thorsten Emig^{3, 2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017, pp.033201Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szeg\"o formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface Renormalization Group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.

- 1. Equipe 106, IJL - Groupe de Physique statistique = Statistical Physics Group [Institut Jean Lamour]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Massachussetts Institute of Technology

## First Gap Statistics of Long Random Walks with Bounded Jumps

### Philippe Mounaix

^{1}Gregory Schehr^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2017, 50 (18), pp.185001We study one-dimensional discrete as well as continuous time random walks, either with a fixed number of steps (for discrete time) $n$ or on a fixed time interval $T$ (for continuous time). In both cases, we focus on symmetric probability distribution functions (PDF) of jumps with a finite support $[-g_{max}, g_{max}]$. For continuous time random walks (CTRWs), the waiting time $\tau$ between two consecutive jumps is a random variable whose probability distribution (PDF) has a power law tail $\Psi(\tau) \propto \tau^{-1-\gamma}$, with $0<\gamma<1$. We obtain exact results for the joint statistics of the gap between the first two maximal positions of the random walk and the time elapsed between them. We show that for large $n$ (or large time $T$ for CTRW), this joint PDF reaches a stationary joint distribution which exhibits an interesting concentration effect in the sense that a gap close to its maximum possible value, $g\approx g_{max}$, is much more likely to be achieved by two successive jumps rather than by a long walk between the first two maxima. Our numerical simulations confirm this concentration effect.

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

## Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures

### Betzalel Bazak

^{1}Dmitry S. Petrov^{2, 3}*Physical Review Letters*, American Physical Society, 2017, 118 (8), pp.083002We show that four heavy fermions interacting resonantly with a lighter atom (4+1 system) become Efimovian at mass ratio 13.279(2), which is smaller than the corresponding 2+1 and 3+1 thresholds. We thus predict the five-body Efimov effect for this system in the regime where any of its subsystem is non- Efimovian. For smaller mass ratios we show the existence and calculate the energy of a universal 4+1 pentamer state, which continues the series of the 2+1 trimer predicted by Kartavtsev and Malykh and 3+1 tetramer discovered by Blume. We also show that the effective-range correction for the light-heavy interaction has a strong effect on all these states and larger effective ranges increase their tendency to bind.

- 1. IPNO - Institut de Physique Nucléaire d'Orsay
- 2. Kavli Institute for Theoretical Institute
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions

### Kirill Plekhanov

^{1, 2}Guillaume Roux^{2}Karyn Le Hur^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95, pp.045102The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically non-trivial band structure associated with chiral edge modes (without the presence of a net unit flux in a unit cell), then referring to the quantum anomalous Hall effect. Focusing on (interacting) boson systems in s-wave bands of the lattice, we show how to engineer through the Floquet theory, a quantum phase transition between a uniform superfluid and a BEC (Bose-Einstein Condensate) analog of FFLO (Fulde-Ferrell-Larkin-Ovchinnikov) states, where bosons condense at non-zero wave-vectors. We perform a Ginzburg-Landau analysis of the quantum phase transition on the graphene lattice, and compute observables such as chiral currents and the momentum distribution. The results are supported by exact diagonalization calculations and compared with those of the isotropic situation. The validity of high-frequency expansion in the Floquet theory is also tested using time-dependent simulations for various parameters of the model. Last, we show that the anisotropic choice for the effective vector potential allows a bosonization approach in equivalent ladder (strip) geometries.

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

## Fragmented-condensate solid of dipolar excitons

### S. V. Andreev

^{1, 2, 3}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95 (18), pp.184519. <10.1103/PhysRevB.95.184519>We discuss a possible link between the recently observed macroscopic ordering of ultracold dipolar excitons (MOES) and the phenomenon of supersolidity. In the dilute limit we predict a stable supersolid state for a quasi-one-dimensional system of bosonic dipoles characterized by two-and three-body contact repulsion. We phenomenologically extend our theory to the strongly-correlated regime and find a critical value of the contact interaction parameter at which the supersolid exhibits a quantum phase transition to a fragmented state. The wavelength of the fragmented-condensate solid is defined by the balance between the quantum pressure and the entropy due to fluctuations of the relative phases between the fragments. Our model appears to be in good agreement with the relevant experimental data, including the very recent results on commensurability effect and wavelength of the MOES.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. ITMO - National Research University of Information Technologies, Mechanics and Optics [St. Petersburg]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Genuine localisation transition in a long-range hopping model

### Xiangyu Cao

^{1}Alberto Rosso^{1}Jean-Philippe Bouchaud^{2}Pierre Le Doussal^{3}*Physical Review E*, American Physical Society (APS), 2017, 95 (6), pp.062118We introduce and study a new class of Banded Random Matrix model describing sparse, long range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and mappings to statistical physics models, we establish the phase diagram of the model. A genuine localisation transition, with well defined mobility edges, appears as the hopping rate decreases slower than $\ell^{-2}$, where $\ell$ is the distance. Correspondingly, the decay of the localised states evolves from a standard exponential shape to a stretched exponential and finally to a novel $\exp(-C\ln^\kappa \ell)$ behaviour, with $\kappa > 1$.

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

## Liouville field theory and log-correlated Random Energy Models

### Xiangyu Cao

^{1}Alberto Rosso^{1}Raoul Santachiara^{1}Pierre Le Doussal^{2}Pierre Le Doussal^{2}*Physical Review Letters*, American Physical Society, 2017, 118 (9), pp.090601An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry breaking methods. Operator product expansions in LFT allow to unveil novel universal behaviours of the log-correlated Random Energy class. High precision numerical tests are given.

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

## Long time scaling behaviour for diffusion with resetting and memory

### Denis Boyer

^{1}Martin R. Evans^{2}Satya N. Majumdar^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017, 2017 (2), pp.023208We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory kernel, we show analytically how different asymptotic behaviours of the variance of the particle position emerge at long times. These range from standard diffusive ($\sigma^2 \sim t$) all the way to anomalous ultraslow growth $\sigma^2 \sim \ln \ln t$.

- 1. UNAM - Universidad Nacional Autónoma de México
- 2. SUPA - School of Physics, University of Edinburgh
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Many body heat radiation and heat transfer in the presence of a non-absorbing background medium

### Muller Boris

^{1}Incardone Roberta^{1}Mauro Antezza^{2, 3}Emig Thorsten^{4, 5}Kruger Matthias^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95, pp.085413. <10.1103/PhysRevB.95.085413>Heat radiation and near-field radiative heat transfer can be strongly manipulated by adjusting geometrical shapes, optical properties, or the relative positions of the objects involved. Typically, these objects are considered as embedded in vacuum. By applying the methods of fluctuational electrodynamics, we derive general closed-form expressions for heat radiation and heat transfer in a system of N arbitrary objects embedded in a passive nonabsorbing background medium. Taking into account the principle of reciprocity, we explicitly prove the symmetry and positivity of transfer in any such system. Regarding applications, we find that the heat radiation of a sphere as well as the heat transfer between two parallel plates is strongly enhanced by the presence of a background medium. Regarding near- and far-field transfer through a gas like air, we show that a microscopic model (based on gas particles) and a macroscopic model (using a dielectric contrast) yield identical results. We also compare the radiative transfer through a medium like air and the energy transfer found from kinetic gas theory.

- 1. Max Planck Institute for Intelligent Systems
- 2. L2C - Laboratoire Charles Coulomb
- 3. Théorie du rayonnement matière et phénomènes quantiques
- 4. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Mean-field avalanches in jammed spheres

### Silvio Franz

^{1}Stefano Spigler^{1}*Physical Review E*, American Physical Society (APS), 2017, 95 (2), pp.022139Disordered systems are characterized by the existence of many sample- dependent local energy minima, that cause a stepwise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three dimensional systems of soft-spheres, either at jamming or at slightly higher densities.

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

## Modification of the Porter-Thomas distribution by rank-one interaction

### E. Bogomolny

^{1}*Physical Review Letters*, American Physical Society, 2017, 118 (2), pp.022501The Porter-Thomas (PT) distribution of resonance widths is one of the oldest and simplest applications of statistical ideas in nuclear physics. Previous experimental data confirmed it quite well but recent and more careful investigations show clear deviations from this distribution. To explain these discrepancies the authors of [PRL \textbf{115}, 052501 (2015)] argued that to get a realistic model of nuclear resonances is not enough to consider one of the standard random matrix ensembles which leads immediately to the PT distribution but it is necessary to add a rank-one interaction which couples resonances to decay channels. The purpose of the paper is to solve this model analytically and to find explicitly the modifications of the PT distribution due to such interaction. Resulting formulae are simple, in a good agreement with numerics, and could explain experimental results.

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

## Non-equilibrium Fluctuational Quantum Electrodynamics: Heat Radiation, Heat Transfer, and Force

### G. Bimonte

^{1, 2}T. Emig^{3, 4}M. Kardar^{3}M. Krüger^{5}*Annual Review of Condensed Matter Physics*, 2017, 8, pp.119Quantum and thermal fluctuations of electromagnetic waves are the cornerstone of quantum and statistical physics, and inherent to such phenomena as thermal radiation and van der Waals forces. While the basic principles are the material of elementary texts, recent experimental and technological advances have made it necessary to come to terms with counterintuitive consequences of electromagnetic fluctuations at short scales -- in the so called {\it near-field} regime. We focus on three manifestations of such behavior: {\bf (i)} The Stefan--Boltzmann law describes thermal radiation from macroscopic bodies, but fails to account for magnitude, polarization and coherence of radiation from small objects (say compared to the skin depth). {\bf (ii)} The heat transfer between two bodies at similar close proximity is dominated by evanescent waves, and can be several orders of magnitude larger than the classical contribution due to propagating waves. {\bf (iii)} Casimir/van der Waals interactions are a dominant force between objects at sub-micron separation; the non-equilibrium analogs of this force (for objects at different temperatures) have not been sufficiently explored (at least experimentally). To explore these phenomena we introduce the tool of fluctuational quantum electrodynamics (QED) originally introduced by Rytov in the 1950s. Combined with a scattering formalism, this enables studies of heat radiation and transfer, equilibrium and non-equilibrium forces for objects of different material properties, shapes, separations and arrangements.

- 1. Università degli studi di Napoli Federico II
- 2. INFN, Sezione di Napoli - Istituto Nazionale di Fisica Nucleare, Sezione di Napoli
- 3. MIT - Massachusetts Institute of Technology
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Max Planck Institute for Intelligent Systems

## P-wave superfluidity of atomic lattice fermions

### A. K. Fedorov

^{1, 2}V. I. Yudson^{3, 1}G. V. Shlyapnikov^{4, 5, 1, 2, 6}*Physical Review A*, American Physical Society, 2017, 95 (4), pp.043615We discuss the emergence of p-wave superfluidity of identical atomic fermions in a two-dimensional optical lattice. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermion sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, for moderate lattice depths the enhancement of the density of states can compensate the decrease of the scattering amplitude. Moreover, the lattice setup significantly reduces inelastic collisional losses, which allows one to get closer to a p-wave Feshbach resonance. This opens possibilities to obtain the topological $p_x+ip_y$ superfluid phase, especially in the recently proposed subwavelength lattices. We demonstrate this for the two-dimensional version of the Kronig-Penney model allowing a transparent physical analysis.

- 1. Russian Quantum Center
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. National Research University Higher School of Economics [Moscow]
- 4. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 5. Wuhan Institute of Physics and Mathematics
- 6. SPEC - UMR3680 - Service de physique de l'état condensé

## Pedestrian flows through a narrow doorway: Effect of individual behaviours on the global flow and microscopic dynamics

### Alexandre Nicolas

^{1, 2}Sebastián Bouzat^{2}Marcelo Kuperman^{3, 2}*Transportation Research Part B: Methodological*, Elsevier, 2017We study the dynamics of pedestrian evacuations through a narrow doorway by means of controlled experiments. The influence of the pedestrians' behaviours is investigated by prescribing a selfish attitude to a fraction c_s of the participants, while the others behave politely. Thanks to an original setup enabling the re-injection of egressed participants into the room, the analysis is conducted in a (macroscopically) quasi-stationary regime. We find that, as c_s is increased, the flow rate J rises, interpolating between published values for egresses in normal conditions and measurements for competitive evacuations. The dependence of several flow properties on the pedestrian density ρ at the door, independently of c_s , suggests that macroscopically the behavioural aspects could be subsumed under the density, at least in our specific settings with limited crowd pressure. In particular, under these conditions, J grows monotonically with ρ up to " close-packing " (ρ ≈ 9 pers/m²). The flow is then characterised microscopically. Among other quantities, the time lapses between successive escapes, the pedestrians' waiting times in front of the door, and their angles of incidence are analysed statistically. In a nutshell, our main results show that the flow is orderly for polite crowds, with narrowly distributed time lapses between egresses, while for larger c_s the flow gets disorderly and vanishing time lapses emerge. For all c_s , we find an alternation between short and long time lapses, which we ascribe to a generalised zipper effect. The average waiting time in the exit zone increases with its occupancy. The disorder in the flow and the pressure felt by participants are also assessed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centre Atomico Bariloche, CNEA and CONICET
- 3. Instituto Balseiro

## Periodic Airy process and equilibrium dynamics of edge fermions in a trap

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}*Annals of Physics*, 2017, 383, pp.312 - 345We establish an exact mapping between (i) the equilibrium (imaginary time) dynamics of non-interacting fermions trapped in a harmonic potential at temperature $T=1/\beta$ and (ii) non-intersecting Ornstein-Uhlenbeck (OU) particles constrained to return to their initial positions after time $\beta$. Exploiting the determinantal structure of the process we compute the universal correlation functions both in the bulk and at the edge of the trapped Fermi gas. The latter corresponds to the top path of the non-intersecting OU particles, and leads us to introduce and study the time-periodic Airy$_2$ process, ${\cal A}^b_2(u)$, depending on a single parameter, the period $b$. The standard Airy$_2$ process is recovered for $b=+\infty$. We discuss applications of our results to the real time quantum dynamics of trapped fermions.

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

## Pickands’ constant at first order in an expansion around Brownian motion

### Mathieu Delorme

^{1}Alberto Rosso^{2}Kay Jörg Wiese^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2017, 50, pp.16LT04In the theory of extreme values of Gaussian processes, many results are expressed in terms of the Pickands constant $\mathcal{H}_{\alpha}$. This constant depends on the local self-similarity exponent $\alpha$ of the process, i.e. locally it is a fractional Brownian motion (fBm) of Hurst index $H=\alpha/2$. Despite its importance, only two values of the Pickands constant are known: ${\cal H}_1 =1$ and ${\cal H}_2=1/\sqrt{\pi}$. Here, we extend the recent perturbative approach to fBm to include drift terms. This allows us to investigate the Pickands constant $\mathcal{H}_{\alpha}$ around standard Brownian motion ($\alpha =1$) and to derive the new exact result $\mathcal{H}_{\alpha}=1 - (\alpha-1) \gamma_{\rm E} + \mathcal{O}\!\left( \alpha-1\right)^{2}$.

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

## Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

### Trithep Devakul

^{1}Satya N. Majumdar^{2}David A. Huse^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95 (10), pp.104204We calculate the probability distribution of entanglement entropy S across a cut of a finite one dimensional spin chain of length L at an infinite randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form $p(S|L) \sim L^{-\psi(k)}$, where $k = S / \log [L/L_0]$, the large deviation function $\psi(k)$ is found explicitly, and $L_0$ is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix product state (MPS) based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

- 1. DPPU - Department of Physics,Princeton University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Quasi-universality in mixed salt-free counterions systems

### M. Trulsson

^{1}Ladislav Šamaj^{2}E. Trizac^{1}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017, 118 (1), pp.16001The screening of plate-plate interactions by counterions is an age-old problem. We revisit this classic question when counterions exhibit a distribution of charges. While it is expected that the long-distance regime of interactions is universal, the behaviour of the inter-plate pressure at smaller distances should a priori depend rather severely on the nature of the ionic mixture screening the plate charges. We show that is not the case, and that for comparable Coulombic couplings, different systems exhibit a quasi-universal equation of state.

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

## Scaling Description of Non-Local Rheology

### Thomas Gueudré

^{1}Jie Lin^{2}Alberto Rosso^{3}Matthieu Wyart^{4}*Soft Matter*, Royal Society of Chemistry, 2017, 13, pp.3794Non-locality is crucial to understand the plastic flow of an amorphous material, and has been successfully described by the fluidity, along with a cooperativity length scale {\xi}. We demonstrate, by applying the scaling hypothesis to the yielding transition, that non-local effects in non-uniform stress configurations can be explained within the framework of critical phenomena. From the scaling description, scaling relations between different exponents are derived, and collapses of strain rate profiles are made both in shear driven and pressure driven flow. We find that the cooperative length in non-local flow is governed by the same correlation length in finite dimensional homogeneous flow, excluding the mean field exponents. We also show that non-locality also affects the finite size scaling of the yield stress, especially the large finite size effects observed in pressure driven flow. Our theoretical results are nicely verified by the elasto-plastic model, and experimental data.

- 1. Polito - Politecnico di Torino [Torino]
- 2. DEPARTMENT OF PHYSICS - New York University
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Institute of Theoretical Physics, Ecole Polytechnique Fédérale, de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

## Search in Patchy Media: Exploration-Exploitation Tradeoff

### M. Chupeau

^{1, 2}O. Bénichou^{2}S. Redner^{3, 4}*Physical Review E*, American Physical Society (APS), 2017, 95 (1), pp.012157How to best exploit patchy resources? This long-standing question belongs to the extensively studied class of explore/exploit problems that arise in a wide range of situations, from animal foraging, to robotic exploration, and to human decision processes. Despite its broad relevance, the issue of optimal exploitation has previously only been tackled through two paradigmatic limiting models---patch-use and random search---that do not account for the interplay between searcher motion within patches and resource depletion. Here, we bridge this gap by introducing a minimal patch exploitation model that incorporates this coupling: the searcher depletes the resources along its random-walk trajectory within a patch and travels to a new patch after it takes $\mathcal{S}$ consecutive steps without finding resources. We compute the distribution of the amount of resources $F_t$ consumed by time $t$ for this non-Markovian random walker and show that exploring multiple patches is beneficial. In one dimension, we analytically derive the optimal strategy to maximize $F_t$. We show that this strategy is robust with respect to the distribution of resources within patches and the criterion for leaving a given patch. We also show that $F_t$ can be optimized in the ecologically-relevant case of two-dimensional patchy environments.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
- 3. BU - Boston University [Boston]
- 4. Santa Fe Institute

## Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation

### Vladimir Belavin

^{1, 2}Xiangyu Cao^{3}Benoit Estienne^{4}Raoul Santachiara^{3}*Journal of High Energy Physics*, Springer, 2017, 3, pp.008In a recent study we considered W3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl3. We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

- 1. P. N. Lebedev Physical Institute of the Russian Academy of Sciences
- 2. IITP - Institute for Information Transmission Problems
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. LPTHE - Laboratoire de Physique Théorique et Hautes Energies

## Shape of the magnetoroton at $\nu=1/3$ and $\nu=7/3$ in real samples

### Thierry Jolicoeur

^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95, pp.075201We revisit the theory of the collective neutral excitation mode in the fractional quantum Hall effect at Landau level filling fractions $\nu=1/3$ and $\nu=7/3$. We include the effect of finite thickness of the two-dimensional electron gas and use extensive exact diagonalizations in the torus geometry. In the lowest Landau level the collective gapped mode i.e. the magnetoroton always merges in the continuum in the long-wavelength limit. In the second Landau level the mode is well-defined only for wavevectors smaller than a critical value and disappears in the continuum beyond this point. Its curvature near zero momentum is opposite to that of the LLL. It is well separated from the continuum even at zero momentum and the gap of the continuum of higher-lying states is twice the collective mode gap at $k=0$. The shape of the dispersion relation survives a perturbative treatment of Landau level mixing.

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

## Spatio-temporal patterns in ultra-slow domain wall creep dynamics

### Ezequiel E. Ferrero

^{1}Laura Foini^{2}Thierry Giamarchi^{2}Alejandro B. Kolton^{3}Alberto Rosso^{4}*Physical Review Letters*, American Physical Society, 2017, 118 (14), pp.147208In presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps, called avalanches, while, at much smaller field, these interfaces creep by thermal activation. In this work we develop a novel numerical technique that captures the ultra-slow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatio-temporal patterns that resemble the complex sequence of aftershocks observed after a large earthquake. Remarkably, we show that events assembly in independent clusters that display at large scales the same statistics as critical depinning avalanches. We foresee this correlated dynamics being experimentally accessible by magneto-optical imaging of ferromagnetic films.

- 1. LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
- 2. Department of Quantum Matter Physics
- 3. CONICET
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya. N. Majumdar^{3}Gregory Schehr^{3, *}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2017, 2017 (6), pp.063301 (1-39). <10.1088/1742-5468/aa6dda>We consider N non-interacting fermions in an isotropic d-dimensional harmonic trap. We compute analytically the cumulative distribution of the maximal radial distance of the fermions from the trap center at zero temperature. While in d = 1 the limiting distribution (in the large N limit), properly centered and scaled, converges to the squared Tracy–Widom distribution of the Gaussian unitary ensemble in random matrix theory, we show that for all d > 1, the limiting distribution converges to the Gumbel law. These limiting forms turn out to be universal, i.e. independent of the details of the trapping potential for a large class of isotropic trapping potentials. We also study the position of the right-most fermion in a given direction in d dimensions and, in the case of a harmonic trap, the maximum momentum, and show that they obey similar Gumbel statistics. Finally, we generalize these results to low but finite temperature.

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

## Temperature Distribution and Heat Radiation of Patterned Surfaces at Short Wave Lengths

### Thorsten Emig

^{1, 2}*Physical Review E*, American Physical Society (APS), 2017, 95 (5), pp.052104We analyze the equilibrium spatial distribution of surface temperatures of patterned surfaces. The surface is exposed to a constant external heat flux and has a fixed internal temperature that is coupled to the outside heat fluxes by finite heat conductivity across surface. It is assumed that the temperatures are sufficiently high so that the thermal wavelength (a few microns at room temperature) is short compared to all geometric length scales of the surface patterns. Hence the radiosity method can be employed. A recursive multiple scattering method is developed that enables rapid convergence to equilibrium temperatures. While the temperature distributions show distinct dependence on the detailed surface shapes (cuboids and cylinder are studied), we demonstrate robust universal relations between the mean and the standard deviation of the temperature distributions and quantities that characterize overall geometric features of the surface shape.

- 1. MIT - Massachusetts Institute of Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The open XXX spin chain in the SoV framework: scalar product of separate states

### N. Kitanine

^{1}J.M. Maillet^{2}G. Niccoli^{2}V. Terras^{3}*J.Phys.*, 2017, <10.1088/1751-8121/aa6cc9>We consider the XXX open spin-1/2 chain with the most general non-diagonal boundary terms, that we solve by means of the quantum separation of variables (SoV) approach. We compute the scalar products of separate states, a class of states which notably contains all the eigenstates of the model. As usual for models solved by SoV, these scalar products can be expressed as some determinants with a non-trivial dependance in terms of the inhomogeneity parameters that have to be introduced for the method to be applicable. We show that these determinants can be transformed into alternative ones in which the homogeneous limit can easily be taken. These new representations can be considered as generalizations of the well-known determinant representation for the scalar products of the Bethe states of the periodic chain. In the particular case where a constraint is applied on the boundary parameters, such that the transfer matrix spectrum and eigenstates can be characterized in terms of polynomial solutions of a usual T-Q equation, the scalar product that we compute here corresponds to the scalar product between two off-shell Bethe-type states. If in addition one of the states is an eigenstate, the determinant representation can be simplified, hence leading in this boundary case to direct analogues of algebraic Bethe ansatz determinant representations of the scalar products for the periodic chain.

- 1. UB - Université de Bourgogne
- 2. ENS Lyon - École normale supérieure - Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Three-dimensional resistivity switching between correlated electronic states in 1T-TaS2

### Damjan Svetin

^{1}Igor Vaskivskyi^{2}Serguei Brazovskii^{3}Dragan Mihailovic^{4, 1, 2}*Scientific Reports*, Nature Publishing Group, 2017, 7, pp.46048Recent demonstrations of controlled switching between different ordered macroscopic states by impulsive electromagnetic perturbations in complex materials have opened some fundamental questions on the mechanisms responsible for such remarkable behavior. Here we experimentally address the question of whether two-dimensional (2D) Mott physics can be responsible for unusual switching between states of different electronic order in the layered dichalcogenide 1T-TaS2, or it is a result of subtle inter-layer orbitronic re-ordering of its helical stacking structure. We report on the switching properties both in-plane and perpendicular to the layers by current-pulse injection, the anisotropy of electronic transport in the commensurate ground state, and relaxation properties of the switched metastable state. Contrary to recent theoretical calculations, which predict a uni-directional metal perpendicular to the layers, we observe a large resistivity in this direction, with a temperature-dependent anisotropy. Remarkably, large resistance ratios are observed in the memristive switching both in-plane (IP) and out-of-plane (OP). The relaxation dynamics of the metastable state for both IP and OP electron transport are seemingly governed by the same mesoscopic quantum re-ordering process. We conclude that 1T-TaS2 shows resistance switching arising from an interplay of both IP and OP correlations.

- 1. Department of Complex Matter
- 2. University of Ljubljana
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. CENN Nanocenter

## Truncated linear statistics associated with the eigenvalues of random matrices II. Partial sums over proper time delays for chaotic quantum dots

### Aurélien Grabsch

^{1}Satya N. Majumdar^{1}Christophe Texier^{1}*Journal of Statistical Physics*, Springer Verlag, 2017, 167 (6), pp.1452 - 1488Invariant ensembles of random matrices are characterized by the distribution of their eigenvalues $\{\lambda_1,\cdots,\lambda_N\}$. We study the distribution of truncated linear statistics of the form $\tilde{L}=\sum_{i=1}^p f(\lambda_i)$ with $p

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

## Truncated linear statistics associated with the top eigenvalues of random matrices

### Aurélien Grabsch

^{1}Satya N. Majumdar^{1}Christophe Texier^{1}*Journal of Statistical Physics*, Springer Verlag, 2017, 167 (2), pp.234 - 259Given a certain invariant random matrix ensemble characterised by the joint probability distribution of eigenvalues $P(\lambda_1,\cdots,\lambda_N)$, many important questions have been related to the study of linear statistics of eigenvalues $L=\sum_{i=1}^Nf(\lambda_i)$, where $f(\lambda)$ is a known function. We study here truncated linear statistics where the sum is restricted to the $N_1

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

## Two- and three-body problem with Floquet-driven zero-range interactions

### A. G. Sykes

^{1}H. Landa^{1}D. S. Petrov^{1}*Physical Review A*, American Physical Society, 2017, 95 (6), pp.062705We study the two-body scattering problem in the zero-range approximation with a sinusoidally driven scattering length and calculate the relation between the mean value and amplitude of the drive for which the effective scattering amplitude is resonantly enhanced. In this manner we arrive at a family of curves along which the effective scattering length diverges but the nature of the corresponding Floquet-induced resonance changes from narrow to wide. Remarkably, on these curves the driving does not induce heating. In order to study the effect of these resonances on the three-body problem we consider one light and two heavy particles with driven heavy-light interaction in the Born-Oppenheimer approximation and find that the Floquet driving can be used to tune the three-body and inelasticity parameters.

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

## Two-body relaxation of spin-polarized fermions in reduced dimensionalities near a p-wave Feshbach resonance

### D. V. Kurlov

^{1}G. V. Shlyapnikov^{2}*Physical Review A*, American Physical Society, 2017, 95 (3), pp.032710We study inelastic two-body relaxation in a spin-polarized ultracold Fermi gas in the presence of a p-wave Feshbach resonance. It is shown that in reduced dimensionalities, especially in the quasi-one-dimensional case, the enhancement of the inelastic rate constant on approach to the resonance is strongly suppressed compared to three dimensions. This may open promising paths for obtaining novel many-body states.

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

## Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

### Pierfrancesco Urbani

^{1}Francesco Zamponi^{2}Silvio Franz^{3}Giorgio Parisi^{4}Maksim Sevelev^{3}*SciPost Physics*, 2017, 2 (3), pp.019Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been studied often involve discrete degrees of freedom: standard random CSPs are random K-SAT (aka disordered Ising models) or random coloring problems (aka disordered Potts models). In this work we consider instead problems that involve continuous degrees of freedom. The simplest prototype of these problems is the perceptron. Here we discuss in detail the full phase diagram of the model. In the regions of parameter space where the problem is non-convex, leading to multiple disconnected clusters of solutions, the solution is critical at the SAT/UNSAT threshold and lies in the same universality class of the jamming transition of soft spheres. We show how the critical behavior at the satisfiability threshold emerges, and we compute the critical exponents associated to the approach to the transition from both the SAT and UNSAT phase. We conjecture that there is a large universality class of non-convex continuous CSPs whose SAT-UNSAT threshold is described by the same scaling solution.

- 1. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Dipartimento di Fisica [Roma]