# 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

## 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

## 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

## 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

### Boris Müller

^{1, 2}Roberta Incardone^{2, 1}Mauro Antezza^{3, 4}Thorsten Emig^{5, 6}Matthias Krüger^{2, 1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2017, 95, pp.085413Heat 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 non-absorbing 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. University of Stuttgart
- 2. Max Planck Institute for Intelligent Systems
- 3. L2C - Laboratoire Charles Coulomb
- 4. IUF - Institut Universitaire de France
- 5. Massachussetts Institute of Technology
- 6. 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

## 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

## 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

## 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