# LPTMS Publications

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## A conformal bootstrap approach to critical percolation in two dimensions

### Marco Picco

^{1}Sylvain Ribault^{2}Raoul Santachiara^{3}*SciPost Physics*, 2016, <10.21468/SciPostPhys.1.1.009>We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.

- 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

## A Materials Perspective on Casimir and van der Waals Interactions

### L. M. Woods

^{1}D. A. R. Dalvit^{2}A. Tkatchenko^{3, 4}P. Rodriguez-Lopez^{5}A. W. Rodriguez^{6}R. Podgornik^{7, 8, 9}*Reviews of Modern Physics*, American Physical Society, 2016, 88, pp.045003Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems with finite dimensions. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nano-structured devices. In the past decade, many new materials have become available, which has stimulated the need of understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insights in related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed matter physics, high energy physics, chemistry and biology. In this review, we summarize major breakthroughs and emphasize the common origin of van der Waals and Casimir interactions. We examine progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter. The outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications.

- 1. USF - University of South Florida
- 2. Theoretical Division [LANL]
- 3. FHI - Fritz-Haber-Institut der Max-Planck-Gesellschaft [Berlin]
- 4. University of Luxembourg [Luxembourg]
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. Princeton University, Princeton, NJ 08544, USA
- 7. University of Massachusetts
- 8. IJS - Jozef Stefan Institute [Ljubljana, Slovenia]
- 9. University of Ljubljana (SLOVENIA)

## Anisotropic collisions of dipolar Bose–Einstein condensates in the universal regime

### Nathaniel Q Burdick

^{1}Andrew G Sykes^{2}Yijun Tang^{1}Benjamin L Lev^{1}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2016, 18 (11), pp.113004- 1. Stanford University [Stanford]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Anisotropic Expansion of a Thermal Dipolar Bose Gas

### Y. Tang

^{1, 2}A. g. Sykes^{3}N. q. Burdick^{2, 1}J. m. Disciacca^{2, 1}D. s. Petrov^{3}B. l. Lev^{2, 1}*Physical Review Letters*, American Physical Society, 2016, 117 (15), pp.155301- 1. Edward L Ginzton Laboratory
- 2. Stanford University [Stanford]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Antiperiodic dynamical 6-vertex model by separation of variables II: functional equations and form factors

### Damien Levy-Bencheton

^{1}Giuliano Niccoli^{2}Véronique Terras^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, 2016 (3), <http://iopscience.iop.org/article/10.1088/1742-5468/2016/03/033110/meta>. <10.1088/1742-5468/2016/03/033110>We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of the antiperiodic transfer matrix are completely characterized by a system of discrete equations. We prove the existence of different reformulations of this characterization in terms of functional equations of Baxter's type. We notably consider the homogeneous functional T-Q equation which is the continuous analog of the aforementioned discrete system and show, in the case of a model with an even number of sites, that the complete spectrum and eigenstates of the antiperiodic transfer matrix can equivalently be described in terms of a particular class of its Q-solutions, hence leading to a complete system of Bethe equations. Finally, we compute the form factors of local operators for which we obtain determinant representations in finite volume.

- 1. IMB - Institut de Mathématiques de Bourgogne
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Asymptotic control theory for a system of linear oscillators

### Aleksey Fedorov

^{1}Alexander Ovseevich^{2}*Moscow mathematical journal*, 2016, 16 (3), pp.561We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna-Lions theory of singular ODEs, we prove that the suggested control law correctly defines the motion of the system. The obtained control is asymptotically optimal: the ratio of the motion time to zero under this control to the minimum one is close to 1 if the initial energy of the system is large. The results are partially based on a new perturbation theory of observable linear systems.

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

## Average diagonal entropy in nonequilibrium isolated quantum systems

### Olivier Giraud

^{1}Ignacio García-Mata^{2}*Physical Review E*, American Physical Society (APS), 2016, 94 (1), pp.012122- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Instituto de Investigaciones Físicas de Mar del Plata

## Bending stiff charged polymers: the electrostatic persistence length

### E. Trizac

^{1}T. Shen^{2}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2016, 116, pp.18007- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. The University of Tennessee [Knoxville]

## Bidirectional imperfect quantum teleportation with a single Bell state

### E. O. Kiktenko

^{1, 2}A. A. Popov^{2}A. K. Fedorov^{3, 4}*Physical Review A*, American Physical Society, 2016, 93, pp.062305We present a bidirectional modification of the standard one-qubit teleportation protocol, where both Alice and Bob transfer noisy versions of their qubit states to each other by using single Bell state and auxiliary (trigger) qubits. Three schemes are considered: the first where the actions of parties are governed by two independent quantum random triggers, the second with single random trigger, and the third as a mixture of the first two. We calculate the fidelities of teleportation for all schemes and find a condition on correlation between trigger qubits in the mixed scheme which allows us to overcome the classical fidelity boundary of 2/3. We apply the Choi-Jamiolkowski isomorphism to the quantum channels obtained in order to investigate an interplay between their ability to transfer the information, entanglement-breaking property, and auxiliary classical communication needed to form correlations between trigger qubits. The suggested scheme for bidirectional teleportation can be realized by using current experimental tools.

- 1. Schmidt Institute of Physics of the Earth, RAS Moscou
- 2. Bauman Moscow State Technical University
- 3. Russian Quantum Center
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Composite operators in Cubic Field Theories and Link Overlap Fluctuations in Spin-Glass Models

### Ada Altieri

^{1, 2}Giorgio Parisi^{2}Tommaso Rizzo^{2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 93, pp.024422We present a complete characterization of the fluctuations and correlations of the squared overlap in the Edwards-Anderson Spin-Glass model in zero field. The analysis reveals that the energy-energy correlations (and thus the specific heat) have a different critical behavior than the fluctuations of the link overlap in spite of the fact that the average energy and average link overlap have the same critical properties. More precisely the link-overlap fluctuations are larger than the specific heat according to a computation at first order in the $6-\epsilon$ expansion. An unexpected outcome is that the link-overlap fluctuations have a subdominant power-law contribution characterized by an anomalous logarithmic prefactor which is missing in the specific heat. In order to compute the $\epsilon$ expansion we consider the problem of the renormalization of quadratic composite operators in a generic multicomponent cubic field theory: the results obtained have a range of applicability beyond spin-glass theory.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica and INFM

## Convex hulls of multiple random walks: A large-deviation study

### Timo Dewenter

^{1}Gunnar Claussen^{2, 1}Alexander K. Hartmann^{1}Satya N. Majumdar^{3}*Physical Review E*, American Physical Society (APS), 2016, 94 (5), pp.052120- 1. Institut für Physik
- 2. FH Oldenburg/Ostfriesland/Wilhelmshaven
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Correlation and fluctuation in Random Average Process on an infinite line with a driven tracer

### J. Cividini

^{1}A. Kundu^{2}S. N. Majumdar^{3}D. Mukamel^{1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, pp.053212We study the effect of single biased tracer particle in a bath of other particles performing the random average process (RAP) on an infinite line. We focus on the large time behavior of the mean and the fluctuations of the positions of the particles and also the correlations among them. In the large time t limit these quantities have well-defined scaling forms and grow with time as $\sqrt{t}$. A differential equation for the scaling function associated with the correlation function is obtained and solved perturbatively around the solution for a symmetric tracer. Interestingly, when the tracer is totally asymmetric, further progress is enabled by the fact that the particles behind of the tracer do not affect the motion of the particles in front of it, which leads in particular to an exact expression for the variance of the position of the tracer. Finally, the variance and correlations of the gaps between successive particles are also studied. Numerical simulations support our analytical results.

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

## Correlation functions with fusion-channel multiplicity in W 3 $$ {\mathcal{W}}_3 $$ Toda field theory

### Vladimir Belavin

^{1, 2}Benoit Estienne^{3}Omar Foda^{4}Raoul Santachiara^{5}*Journal of High Energy Physics*, Springer, 2016, 2016 (6), pp.137- 1. IITP - Institute for Information Transmission Problems
- 2. P. N. Lebedev Physical Institute [Moscow]
- 3. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
- 4. University of Melbourne
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Crossing probability for directed polymers in random media. II. exact tail of the distribution

### Andrea De Luca

^{1}Pierre Le Doussal^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.032118. <10.1103/PhysRevE.93.032118>We study the probability $p \equiv p_\eta(t)$ that two directed polymers in a given random potential $\eta$ and with fixed and nearby endpoints, do not cross until time $t$. This probability is itself a random variable (over samples $\eta$) which, as we show, acquires a very broad probability distribution at large time. In particular the moments of $p$ are found to be dominated by atypical samples where $p$ is of order unity. Building on a formula established by us in a previous work using nested Bethe Ansatz and Macdonald process methods, we obtain analytically the leading large time behavior of {\it all moments} $\overline{p^m}\simeq \gamma_m/t$. From this, we extract the exact tail $\sim \rho(p)/t$ of the probability distribution of the non-crossing probability at large time. The exact formula is compared to numerical simulations, with excellent agreement.

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

## Dispersive hydrodynamics of nonlinear polarization waves in two-component Bose-Einstein condensates

### T. Congy

^{1}A. M. Kamchatnov^{2}N. Pavloff^{1}*SciPost Physics*, 2016, 1 (1), pp.006We study one dimensional mixtures of two-component Bose-Einstein condensates in the limit where the intra-species and inter-species interaction constants are very close. Near the mixing-demixing transition the polarization and the density dynamics decouple. We study the nonlinear polarization waves, show that they obey a universal (i.e., parameter free) dynamical description, identify a new type of algebraic soliton, explicitly write simple wave solutions, and study the Gurevich-Pitaevskii problem in this context.

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

## Distribution of spectral linear statistics on random matrices beyond the large deviation function — Wigner time delay in multichannel disordered wires

### Aurélien Grabsch

^{1}Christophe Texier^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49 (20), pp.465002An invariant ensemble of $N\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\lambda_1,\cdots,\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form $L=(1/N)\sum_if(\lambda_i)$ where $f(x)$ is a given function, appears in many physical problems. In the $N\to\infty$ limit, $L$ scales as $L\sim N^\eta$, where the scaling exponent $\eta$ depends on the ensemble and the function $f$. Its distribution can be written under the form $P_N(s=N^{-\eta}\,L)\simeq A_{\beta,N}(s)\,\exp\big\{-(\beta N^2/2)\,\Phi(s)\big\}$, where $\beta\in\{1,\,2,\,4\}$ is the Dyson index. The Coulomb gas technique naturally provides the large deviation function $\Phi(s)$, which can be efficiently obtained thanks to a "thermodynamic identity" introduced earlier. We conjecture the pre-exponential function $A_{\beta,N}(s)$. We check our conjecture on several well controlled cases within the Laguerre and the Jacobi ensembles. Then we apply our main result to a situation where the large deviation function has no minimum (and $L$ has infinite moments)~: this arises in the statistical analysis of the Wigner time delay for semi-infinite multichannel disordered wires (Laguerre ensemble). The statistical analysis of the Wigner time delay then crucially depends on the pre-exponential function $A_{\beta,N}(s)$, which ensures the decay of the distribution for large argument.

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

## Dropping the independence: singular values for products of two coupled random matrices

### Gernot Akemann

^{1, 2}Eugene Strahov^{3}*Communications in Mathematical Physics*, Springer Verlag, 2016, 345 (1), pp.101We study the singular values of the product of two coupled rectangular random matrices as a determinantal point process. Each of the two factors is given by a parameter dependent linear combination of two independent, complex Gaussian random matrices, which is equivalent to a coupling of the two factors via an Itzykson-Zuber term. We prove that the squared singular values of such a product form a biorthogonal ensemble and establish its exact solvability. The parameter dependence allows us to interpolate between the singular value statistics of the Laguerre ensemble and that of the product of two independent complex Ginibre ensembles which are both known. We give exact formulae for the correlation kernel in terms of a complex double contour integral, suitable for the subsequent asymptotic analysis. In particular, we derive a Christoffel-Darboux type formula for the correlation kernel, based on a five term recurrence relation for our biorthogonal functions. It enables us to find its scaling limit at the origin representing a hard edge. The resulting limiting kernel coincides with the universal Meijer G-kernel found by several authors in different ensembles. We show that the central limit theorem holds for the linear statistics of the singular values and give the limiting variance explicitly.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Fakultät für Physik
- 3. HEBREW UNIVERSITY - Dept. Of Mathematics, Hebrew University

## Electromagnetic Casimir energy of a disk opposite a plane

### Thorsten Emig

^{1, 2, 3}Noah Graham^{4}*Physical Review A*, American Physical Society, 2016, 94 (3), pp.032509- 1. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment
- 2. Massachussetts Institute of Technology
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Middlebury College

## Energy transport between two integrable spin chains

### Alberto Biella

^{1, 2}Andrea De Luca^{3}Jacopo Viti^{4}Davide Rossini^{2, 1}Leonardo Mazza^{5, 2}Rosario Fazio^{6, 2, 1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 93, pp.205121We study the energy transport in a system of two half-infinite XXZ chains initially kept separated at different temperatures, and later connected and let free to evolve unitarily. By changing independently the parameters of the two halves, we highlight, through bosonisation and time-dependent matrix-product-state simulations, the different contributions of low-lying bosonic modes and of fermionic quasi-particles to the energy transport. In the simulations we also observe that the energy current reaches a finite value which only slowly decays to zero. The general pictures that emerges is the following. Since integrability is only locally broken in this model, a pre-equilibration behaviour may appear. In particular, when the sound velocities of the bosonic modes of the two halves match, the low-temperature energy current is almost stationary and described by a formula with a non-universal prefactor interpreted as a transmission coefficient. Thermalisation, characterized by the absence of any energy flow, occurs only on longer time-scales which are not accessible with our numerics.

- 1. Kavli Institute for Theoretical Physics
- 2. SNS - Scuola Normale Superiore di Pisa
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. UFRN - Universidade Federal do Rio Grande do Norte [Natal]
- 5. Departement de Physique-ENS
- 6. ICTP - International Center for Theoretical Physics [Trieste]

## Engineered swift equilibration of a Brownian particle

### Ignacio Martinez

^{1}Artyom Petrosyan^{1}David Guéry-Odelin^{2}Emmanuel Trizac^{3}Sergio Ciliberto^{1}*Nature Physics*, Nature Publishing Group, 2016, 12, pp.843-846. <10.1038/nphys3758>A fundamental and intrinsic property of any device or natural system is its relaxation time relax, which is the time it takes to return to equilibrium after the sudden change of a control parameter [1]. Reducing τ relax , is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on driving have been recently demonstrated [2, 3], for isolated quantum and classical systems [4–9]. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol,named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro and nano devices, where the reduction of operation time represents as substantial a challenge as miniaturization [10]. The concepts of equilibrium and of transformations from an equilibrium state to another, are cornerstones of thermodynamics. A textbook illustration is provided by the expansion of a gas, starting at equilibrium and expanding to reach a new equilibrium in a larger vessel. This operation can be performed either very slowly by a piston, without dissipating energy into the environment, or alternatively quickly, letting the piston freely move to reach the new volume.

- 1. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 2. Atomes Froids (LCAR)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Equilibration Properties of Classical Integrable Field Theories

### Andrea De Luca

^{1}Giuseppe Mussardo^{2, 3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, 064011We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper $\hbar \rightarrow 0$ limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the Generalized Gibbs Ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the {\em infinite gap solutions} of the Inverse Scattering Method.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
- 3. ICTP - International Center for Theoretical Physics [Trieste]

## Evidence of spin-temperature in dynamic nuclear polarization: an exact computation of the EPR spectrum

### Filippo Caracciolo

^{1}Marta Filibian^{1}Pietro Carretta^{1}Alberto Rosso^{2}Andrea De Luca^{2}*PCCP : Physical chemistry chemical physics*, Royal Society of Chemistry, 2016, 18, pp.25655In a dynamic nuclear polarization (DNP) procedure, the compound is driven out-of-equilibrium by microwave irradiation of the dipolar electron spins of the radical. The main outcome of this protocol is the huge polarization enhancement for nuclear spins. In this paper, we focus on the steady-state polarization of the electron spins, which is experimentally accessible via ELDOR techniques. By varying the radical concentration, two scenarios emerge: for dilute samples, the irradiated ELDOR spectrum displays the narrow hole-burning profile predicted by Bloch equations; for higher concentrations, the ELDOR spectrum is completely reorganized according to the spin-temperature description. We discuss our results in relation with recent EPR experiments and, in particular, we analyze the dependence on the microwave intensity.

- 1. CNISM - Dipartimento di Fisica and Unità
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Exact distributions of cover times for $N$ independent random walkers in one dimension

### Satya N. Majumdar

^{1}Sanjib Sabhapandit^{2}Gregory Schehr^{1}*Physical Review E*, American Physical Society (APS), 2016, 94 (6), pp.062131We study the probability density function (PDF) of the cover time $t_c$ of a finite interval of size $L$, by $N$ independent one-dimensional Brownian motions, each with diffusion constant $D$. The cover time $t_c$ is the minimum time needed such that each point of the entire interval is visited by at least one of the $N$ walkers. We derive exact results for the full PDF of $t_c$ for arbitrary $N \geq 1$, for both reflecting and periodic boundary conditions. The PDFs depend explicitly on $N$ and on the boundary conditions. In the limit of large $N$, we show that $t_c$ approaches its average value $\langle t_c \rangle \approx L^2/(16\, D \, \ln N)$, with fluctuations vanishing as $1/(\ln N)^2$. We also compute the centered and scaled limiting distributions for large $N$ for both boundary conditions and show that they are given by nontrivial $N$-independent scaling functions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Raman Research Institute

## Exact extreme value statistics at mixed order transitions

### Amir Bar

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}David Mukamel^{1}*Physical Review E*, American Physical Society (APS), 2016, 93, pp.052130We study extreme value statistics (EVS) for spatially extended models exhibiting mixed order phase transitions (MOT). These are phase transitions which exhibit features common to both first order (discontinuity of the order parameter) and second order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising (TIDSI) model which is a prototypical model exhibiting MOT, and study analytically the extreme value statistics of the domain lengths. The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size $L$. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length $l_{\max}$ converges, in the large $L$ limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of $l_{\max}$ are governed by novel distributions which we compute exactly. Our main analytical results are verified by numerical simulations.

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

## Exact gap statistics for the random average process on a ring with a tracer

### Julien Cividini

^{1}Anupam Kundu^{2, 3, 1}Satya N. Majumdar^{3}David Mukamel^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.085002We study statistics of the gaps in Random Average Process (RAP) on a ring with particles hopping symmetrically, except one tracer particle which could be driven. These particles hop either to the left or to the right by a random fraction $\eta$ of the space available till next particle in the respective directions. The random fraction $\eta \in [0,~1)$ is chosen from a distribution $R(\eta)$. For non-driven tracer, when $R(\eta)$ satisfies a necessary and sufficient condition, the stationary joint distribution of the gaps between successive particles takes an universal form that is factorized except for a global constraint. Some interesting explicit forms of $R(\eta)$ are found which satisfy this condition. In case of driven tracer, the system reaches a current-carrying steady state where such factorization does not hold. Analytical progress has been made in the thermodynamic limit, where we computed the single site mass distribution inside the bulk. We have also computed the two point gap-gap correlation exactly in that limit. Numerical simulations support our analytical results.

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

## Exact Short-Time Height Distribution in the One-Dimensional Kardar-Parisi-Zhang Equation and Edge Fermions at High Temperature

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Alberto Rosso^{2}Grégory Schehr^{2}*Physical Review Letters*, American Physical Society, 2016, 117 (7), pp.070403- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Exact statistics of record increments of random walks and L\’evy flights

### Claude Godreche

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}*Physical Review Letters*, American Physical Society, 2016, 117, pp.010601We study the statistics of increments in record values in a time series $\{x_0=0,x_1, x_2, \ldots, x_n\}$ generated by the positions of a random walk (discrete time, continuous space) of duration $n$ steps. For arbitrary jump length distribution, including L\'evy flights, we show that the distribution of the record increment becomes stationary, i.e., independent of $n$ for large $n$, and compute it explicitly for a wide class of jump distributions. In addition, we compute exactly the probability $Q(n)$ that the record increments decrease monotonically up to step $n$. Remarkably, $Q(n)$ is universal (i..e., independent of the jump distribution) for each $n$, decaying as $Q(n) \sim {\cal A}/\sqrt{n}$ for large $n$, with a universal amplitude ${\cal A} = e/\sqrt{\pi} = 1.53362\ldots$.

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

## Extreme value statistics of 2d Gaussian Free Field: effect of finite domains

### Xiangyu Cao

^{1}Alberto Rosso^{1}Raoul Santachiara^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.02LT02We study minima statistics of the 2d Gaussian Free Field on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated Random Energy models are exactly calculated in the high temperature phase, and shown to satisfy the duality property, which enables us to predict the minima distribution by assuming the freezing scenario. Numerical tests are provided. Related questions concerning the GFF on a sphere are also considered.

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

## Fast electronic resistance switching involving hidden charge density wave states

### I. Vaskivskyi

^{1, 2}I. A. Mihailovic^{2, 1}S. Brazovskii^{3, 4}J. Gospodaric^{2}T. Mertelj^{2}D. Svetin^{2}P. Sutar^{2}D. Mihailovic^{5, 2, 1}*Nature Communications*, Nature Publishing Group, 2016, 7, pp.11442- 1. University of Ljubljana
- 2. Department of Complex Matter
- 3. MISIS - National University of Science and Technology
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Jozef Stefan International Postgraduate School [Ljubljana, Slovenia]

## Fast equilibrium switch of a micro mechanical oscillator

### Anne Le Cunuder

^{1}Ignacio Martinez^{1}Artyom Petrosyan^{1}David Guéry-Odelin^{2}Emmanuel Trizac^{3}Sergio Ciliberto^{1}*Applied Physics*, Springer-Verlag, 2016, Applied Physics Letters 109, pp.113502We demonstrate an accurate method to control the motion of a micromechanical oscillator in contact with a thermal bath. The experiment is carried out on the cantilever tip of an Atomic Force Microscope (AFM). Applying an appropriate time dependent external force, we decrease the time necessary to reach equilibrium by two orders of magnitude compared to the intrinsic equilibration time. Finally, we analyze the energetic cost of such a fast equilibration, by measuring with kBT accuracy the energy exchanges along the process.

- 1. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 2. Atomes Froids (LCAR)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Fiber networks amplify active stress

### Pierre Ronceray

^{1}Chase Broedersz^{2, 3}Martin Lenz^{1}*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2016, 113, pp.2827Large-scale force generation is essential for biological functions such as cell motility, embryonic development, and muscle contraction. In these processes, forces generated at the molecular level by motor proteins are transmitted by disordered fiber networks, resulting in large-scale active stresses. While these fiber networks are well characterized macroscopically, this stress generation by microscopic active units is not well understood. Here we theoretically study force transmission in these networks, and find that local active forces are rectified towards isotropic contraction and strongly amplified as fibers collectively buckle in the vicinity of the active units. This stress amplification is reinforced by the networks' disordered nature, but saturates for high densities of active units. Our predictions are quantitatively consistent with experiments on reconstituted tissues and actomyosin networks, and shed light on the role of the network microstructure in shaping active stresses in cells and tissue.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Arnold Sommerfeld Center for Theoretical Physics
- 3. Lewis-Sigler Institute for Integrative Genomics

## Finite N corrections to the limiting distribution of the smallest eigenvalue of Wishart complex matrices

### Anthony Perret

^{1}Gregory Schehr^{1}*Random Matrices. Theory and Applications*, 2016, 5, pp.1650001We study the probability distribution function (PDF) of the smallest eigenvalue of Laguerre-Wishart matrices $W = X^\dagger X$ where $X$ is a random $M \times N$ ($M \geq N$) matrix, with complex Gaussian independent entries. We compute this PDF in terms of semi-classical orthogonal polynomials, which are deformations of Laguerre polynomials. By analyzing these polynomials, and their associated recurrence relations, in the limit of large $N$, large $M$ with $M/N \to 1$ -- i.e. for quasi-square large matrices $X$ -- we show that this PDF, in the hard edge limit, can be expressed in terms of the solution of a Painlev\'e III equation, as found by Tracy and Widom, using Fredholm operators techniques. Furthermore, our method allows us to compute explicitly the first $1/N$ corrections to this limiting distribution at the hard edge. Our computations confirm a recent conjecture by Edelman, Guionnet and P\'ech\'e. We also study the soft edge limit, when $M-N \sim {\cal O}(N)$, for which we conjecture the form of the first correction to the limiting distribution of the smallest eigenvalue.

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

## Finite-temperature effects on interacting bosonic one-dimensional systems in disordered lattices

### Lorenzo Gori

^{1}Thomas Barthel^{2, 3}Avinash Kumar^{1}Eleonora Lucioni^{4, 1}Luca Tanzi^{1}Massimo Inguscio^{1, 4}Giovanni Modugno^{1, 4}Thierry Giamarchi^{5}Chiara D'Errico^{1, 4}Guillaume Roux^{3}*Physical Review A*, American Physical Society, 2016, 93, pp.033650We analyze the finite-temperature effects on the phase diagram describing the insulating properties of interacting 1D bosons in a quasi-periodic lattice. We examine thermal effects by comparing experimental results to exact diagonalization for small-sized systems and to density-matrix renormalization group (DMRG) computations. At weak interactions, we find short thermal correlation lengths, indicating a substantial impact of temperature on the system coherence. Conversely, at strong interactions, the obtained thermal correlation lengths are significantly larger than the localization length, and the quantum nature of the T=0 Bose glass phase is preserved up to a crossover temperature that depends on the disorder strength. Furthermore, in the absence of disorder, we show how quasi-exact finite-T DMRG computations, compared to experimental results, can be employed to estimate the temperature, which is not directly accessible in the experiment.

- 1. European Laboratory for Non-linear Spectroscopy (LENS)
- 2. Duke university [Durham]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. CNR-IFAC, Sesto Fiorentino
- 5. DPMC - Département de Physique de la Matière Condensée

## Finite-temperature fluid–insulator transition of strongly interacting 1D disordered bosons

### Vincent P. Michal

^{1}Igor L. Aleiner^{2}Boris L. Altshuler^{3, 2}Georgy V. Shlyapnikov^{4, 5, 1, 3}*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2016, 113 (31), pp.E4455 - E4459- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Columbia University [New York]
- 3. Wuhan Institute of Physics and Mathematics
- 4. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 5. Russian Quantum Center

## Formation of exciton rings and localized bright spots in coupled semiconductor quantum wells

### S. V. Andreev

^{1, 2, 3, *}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (16), pp.165308 (1-6). <10.1103/PhysRevB.94.165308>We consider indirect excitons generated at the ring-shaped boundaries between electron-and hole-rich regions in semiconductor quantum wells (QW's). We show theoretically that the in-plane translational motion of the excitons is confined in the radial direction. The confinement potential results from the electrostatic interaction of the exciton dipole moment with the in-plane electric field induced at the boundary by the macroscopic charge separation. Our results directly apply to the external ring and the localized bright spots (LBS) observed in the photoluminescense (PL) pattern of indirect excitons.

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

## Four-terminal resistances in mesoscopic networks of metallic wires: Weak localisation and correlations

### Christophe Texier

^{1}Gilles Montambaux^{2}*Physica E: Low-dimensional Systems and Nanostructures*, Elsevier, 2016, 75, pp.33We consider the electronic transport in multi-terminal mesoscopic networks of weakly disordered metallic wires. After a brief description of the classical transport, we analyze the weak localisation (WL) correction to the four-terminal resistances, which involves an integration of the Cooperon over the wires with proper weights. We provide an interpretation of these weights in terms of classical transport properties. We illustrate the formalism on examples and show that weak localisation to four-terminal conductances may become large in some situations. In a second part, we study the correlations of four-terminal resistances and show that integration of Diffuson and Cooperon inside the network involves the same weights as the WL. The formulae are applied to multiconnected wire geometries.

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

## From liquid structure to configurational entropy: introducing structural covariance

### Pierre Ronceray

^{1}Peter Harrowell^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, 2016 (8), pp.084002- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Faculty of Sciences

## Identifying relevant positions in proteins by Critical Variable Selection

### Silvia Grigolon

^{1}Silvio Franz^{1}Matteo Marsili^{2}*Molecular BioSystems*, Royal Society of Chemistry, 2016, 12, pp.2147Evolution in its course found a variety of solutions to the same optimisation problem. The advent of high-throughput genomic sequencing has made available extensive data from which, in principle, one can infer the underlying structure on which biological functions rely. In this paper, we present a new method aimed at extracting sites encoding structural and func- tional properties from a set of protein primary sequences, namely a Multiple Sequence Alignment. The method, called Critical Variable Selection, is based on the idea that subsets of relevant sites cor- respond to subsequences that occur with a particularly broad frequency distribution in the dataset. By applying this algorithm to in silico sequences, to the Response Regulator Receiver and to the Voltage Sensor Domain of Ion Channels, we show that this procedure recovers not only information encoded in single site statistics and pairwise correlations but it also captures dependencies going beyond pairwise correlations. The method proposed here is complementary to Statistical Coupling Analysis, in that the most relevant sites predicted by the two methods markedly differ. We find robust and consistent results for datasets as small as few hundred sequences, that reveal a hidden hierarchy of sites that is consistent with present knowledge on biologically relevant sites and evo- lutionary dynamics. This suggests that Critical Variable Selection is able to identify in a Multiple Sequence Alignment a core of sites encoding functional and structural information.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. ICTP - International Center for Theoretical Physics [Trieste]

## Information processing using three-qubit and qubit-qutrit encodings of noncomposite quantum systems

### A. A. Popov

^{1}E. O. Kiktenko^{1}A. K. Fedorov^{2, 3}V. I. Man'Ko^{4, 5}*Journal of Russian Laser Research*, Springer Verlag, 2016, 37, pp.581We study quantum information properties of a seven-level system realized by a particle in an one-dimensional square-well trap. Features of encodings of seven-level systems in a form of three-qubit or qubit-qutrit systems are discussed. We use the three-qubit encoding of the system in order to investigate subadditivity and strong subadditivity conditions for the thermal state of the particle. The qubit-qutrit encoding is employed to suggest a single qudit algorithm for calculation of parity of a bit string. Obtained results indicate on the potential resource of multilevel systems for realization of quantum information processing.

- 1. Bauman Moscow State Technical University
- 2. Russian Quantum Center
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. MIPT - Moscow Institute of Physics and Technology [Moscow]
- 5. P. N. Lebedev Physical Institute of the Russian Academy of Sciences

## Itinerant ferromagnetism in 1D two-component Fermi gases

### Yuzhu Jiang

^{1}D. V. Kurlov^{2}Xi-Wen Guan^{1, 3}F. Schreck^{2}G. V. Shlyapnikov^{4, 1, 2, 5}*Physical Review A*, American Physical Society, 2016, 94, pp.011601We study a one-dimensional two-component atomic Fermi gas with an infinite intercomponent contact repulsion. It is found that adding an attractive resonant odd-wave interaction breaking the rotational symmetry one can make the ground state ferromagnetic. A promising system for the observation of this itinerant ferromagnetic state is a 1D gas of $^{40}$K atoms, where 3D $s$-wave and $p$-wave Feshbach resonances are very close to each other and the 1D confinement significantly reduces the inelastic decay.

- 1. State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071 China
- 2. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 3. Department of Physics, Australian National University
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Russian Quantum Center

## Joint min-max distribution and Edwards-Anderson’s order parameter of the circular 1/f-noise model

### Xiangyu Cao

^{1}Pierre Le Doussal^{2}*EPL*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2016, 114 (4), pp.40003- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Large deviations for the height in 1D Kardar-Parisi-Zhang growth at late times

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}*EPL*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2016, 113, pp.60004We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the rate functions for the discrete single step growth model, as well as for the continuum KPZ equation in a droplet geometry. Based on our exact calculation of the rate functions we argue that models in the KPZ class undergo a third order phase transition from a strong coupling to a weak coupling phase, at late times.

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

## Lifetime of Feshbach dimers in a Fermi-Fermi mixture of $^6$Li and $^{40}$K

### Michael Jag

^{1}Marko Cetina^{2}Rianne S. Lous^{1}Rudolf Grimm^{1}Jesper Levinsen^{3, 4}Dmitry S. Petrov^{5}*Physical Review A*, American Physical Society, 2016, 94 (6), pp.062706- 1. Institut für Experimentalphysik [Innsbruck]
- 2. Institut für Quantenoptik und Quanteninformation
- 3. TCM Group, Cavendish Laboratory
- 4. Aarhus Institute of Advanced Studies
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Mean-field beyond mean-field: the single particle view for moderately to strongly coupled charged fluids

### L. Samaj

^{1}A. P. Dos Santos^{2}Y. Levin^{2}E. Trizac^{3}*Soft Matter*, Royal Society of Chemistry, 2016, 12, pp.8768- 1. INSTITUTE OF PHYSICS - SLOVAK ACADEMY OF SCIENCES Institute of Physics Dubraska cesta 9, 84228 Bratislava, Slovaquie
- 2. UFRGS - Universidade Federal do Rio Grande do Sul [Porto Alegre]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Microscopic origin of self-similarity in granular blast waves

### M. Barbier

^{1}D. Villamaina^{2}E. Trizac^{3}*Physics of Fluids*, American Institute of Physics, 2016, 28 (8), pp.083302- 1. Department of Ecology and Evolutionary Biology [Princeton]
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Native ultrametricity of sparse random ensembles

### V. Avetisov

^{1, 2}P. L. Krapivsky^{3}S. Nechaev^{4, 5}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.035101We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. We demonstrate that the fraction of linear subgraphs just below the percolation threshold is about 95\% of all finite subgraphs, and the distribution of linear chains is purely exponential. We analyze in detail the spectral density of ensembles of linear subgraphs, discuss its ultrametric nature and show that near the spectrum boundary, the tail of the spectral density exhibits a Lifshitz singularity typical for Anderson localization. We also discuss an intriguing connection of the spectral density to the Dedekind $\eta$-function. We conjecture that ultrametricity is inherit to complex systems with extremal sparse statistics and argue that a number-theoretic ultrametricity emerges in any rare-event statistics.

- 1. Department of Applied Mathematics
- 2. The Semenov Institute of Chemical Physics
- 3. Boston University, Boston, Massachusetts, USA
- 4. P. N. Lebedev Physical Institute [Moscow]
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Non Relativistic Limit of Integrable QFT and Lieb-Liniger Models

### Alvise Bastianello

^{1}Andrea De Luca^{2}Giuseppe Mussardo^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, 2016 (12), pp.123104In this paper we study a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda Field Theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.

- 1. SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. ICTP - International Center for Theoretical Physics [Trieste]

## Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Gregory Schehr^{3}Pierre Le Doussal^{2}*Physical Review A*, American Physical Society, 2016, 94 (6), pp.063622We study a system of $N$ non-interacting spin-less fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the trap introduces an edge where the average density of fermions vanishes. Far from the edge, near the center of the trap (the so called "bulk regime"), physical properties of the fermions have traditionally been understood using the Local Density Approximation. However, this approximation drastically fails near the edge where the density vanishes. In this paper we show that, even near the edge, novel universal properties emerge, independently of the details of the confining potential. We show that for large $N$, these fermions in a confining trap, in arbitrary dimensions and at finite temperature, form a determinantal point process. As a result, any $n$-point correlation function can be expressed as an $n \times n$ determinant whose entry is called the kernel. Near the edge, we derive the large $N$ scaling form of the kernels. In $d=1$ and $T=0$, this reduces to the so called Airy kernel, that appears in the Gaussian Unitary Ensemble (GUE) of random matrix theory. In $d=1$ and $T>0$ we show a remarkable connection between our kernel and the one appearing in the $1+1$-dimensional Kardar-Parisi-Zhang equation at finite time. Consequently our result provides a finite $T$ generalization of the Tracy-Widom distribution, that describes the fluctuations of the rightmost fermion at $T=0$. In $d>1$ and $T \geq 0$, while the connection to GUE no longer holds, the process is still determinantal whose analysis provides a new class of kernels, generalizing the $1d$ Airy kernel at $T=0$ obtained in random matrix theory. Some of our finite temperature results should be testable in present-day cold atom experiments, most notably our detailed predictions for the temperature dependence of the fluctuations near the edge.

- 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

## Nonergodic Phases in Strongly Disordered Random Regular Graphs

### B. l. Altshuler

^{1}E. Cuevas^{2}L. b. Ioffe^{3, 4}V. e. Kravtsov^{5, 4}*Physical Review Letters*, American Physical Society, 2016, 117 (15), pp.156601- 1. Columbia University [New York]
- 2. University of Murcia
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. LANDAU INSTITUTE - Landau Institute for Theoretical Physics
- 5. ICTP - International Center for Theoretical Physics [Trieste]

## Noninteracting fermions at finite temperature in a d -dimensional trap: Universal correlations

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Grégory Schehr^{3}*Physical Review A*, American Physical Society, 2016, 94 (6), pp.063622 (1-41). <10.1103/PhysRevA.94.063622>We study a system of $N$ non-interacting spin-less fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the trap introduces an edge where the average density of fermions vanishes. Far from the edge, near the center of the trap (the so called "bulk regime"), physical properties of the fermions have traditionally been understood using the Local Density Approximation. However, this approximation drastically fails near the edge where the density vanishes. In this paper we show that, even near the edge, novel universal properties emerge, independently of the details of the confining potential. We show that for large $N$, these fermions in a confining trap, in arbitrary dimensions and at finite temperature, form a determinantal point process. As a result, any $n$-point correlation function can be expressed as an $n \times n$ determinant whose entry is called the kernel. Near the edge, we derive the large $N$ scaling form of the kernels. In $d=1$ and $T=0$, this reduces to the so called Airy kernel, that appears in the Gaussian Unitary Ensemble (GUE) of random matrix theory. In $d=1$ and $T>0$ we show a remarkable connection between our kernel and the one appearing in the $1+1$-dimensional Kardar-Parisi-Zhang equation at finite time. Consequently our result provides a finite $T$ generalization of the Tracy-Widom distribution, that describes the fluctuations of the rightmost fermion at $T=0$. In $d>1$ and $T \geq 0$, while the connection to GUE no longer holds, the process is still determinantal whose analysis provides a new class of kernels, generalizing the $1d$ Airy kernel at $T=0$ obtained in random matrix theory. Some of our finite temperature results should be testable in present-day cold atom experiments, most notably our detailed predictions for the temperature dependence of the fluctuations near the edge.

- 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

## Nonlinear waves in coherently coupled Bose-Einstein condensates

### T. Congy

^{1}A. Kamchatnov^{2}N. Pavloff^{1}*Physical Review A*, American Physical Society, 2016, 93, pp.043613We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the elementary excitations. The spectrum has two branches which are affected in different ways. The upper branch experiences a modulational instability which is stabilized by a long wave-short wave resonance with the lower branch. The lower branch is stable. In the limit of weak nonlinearity and small dispersion it is described by a Korteweg-de Vries equation or by the Gardner equation, depending on the value of the parameters of the system.

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

## Novel $p$-wave superfluids of fermionic polar molecules

### A. K. Fedorov

^{1, 2}S. I. Matveenko^{3, 2}V. I. Yudson^{4, 1}G. V. Shlyapnikov^{5, 2, 1, 6}*Scientific Reports*, Nature Publishing Group, 2016, 6, pp.27448We show that recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological $p$-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer $p$-wave superfluid of polar molecules in a bilayer geometry.

- 1. Russian Quantum Center
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Landau Institute for Theoretical Physics
- 4. Institute of Spectroscopy
- 5. Wuhan Institute of Physics and Mathematics
- 6. Van der Waals - Zeeman Institute

## Nuclear Magnetic Resonance studies of DNP-ready trehalose obtained by solid state mechanochemical amorphization

### Marta Filibian

^{1}Elena Elisei^{2, 3}Sonia Colombo Serra^{4}Alberto Rosso^{5}Fabio Tedoldi^{4}Attilio Cesàro^{3, 6}Pietro Carretta^{1}*Physical Chemistry Chemical Physics*, Royal Society of Chemistry, 2016, 18, pp.16912- 1. CNISM - Dipartimento di Fisica and Unità
- 2. UMET - Unité Matériaux et Transformations
- 3. Department of Chemical and Pharmaceutical Sciences
- 4. Centro Ricerche Bracco
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. SINCROTRONE TRIESTE - Sincrotrone Trieste SCpA

## Number statistics for β -ensembles of random matrices: Applications to trapped fermions at zero temperature

### Ricardo Marino

^{1}Satya N. Majumdar^{2}Grégory Schehr^{2}Pierpaolo Vivo^{3}*Physical Review E*, American Physical Society (APS), 2016, 94 (3), pp.032115- 1. WIS - Weizmann Institute of Science
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. King's College London

## Occupation time statistics of the random acceleration model

### Hermann Joel Ouandji Boutcheng

^{1, 2}Thomas Bouetou Bouetou^{3, 1}Theodore W. Burkhardt^{4}Alberto Rosso^{5}Andrea Zoia^{6}Kofane Timoleon Crepin^{2, 1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, pp.053213The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are non-trivial and not yet completely understood. In this paper we consider the occupation time $T_+$ of the one-dimensional random acceleration model on the positive half-axis. We calculate the first two moments of $T_+$ analytically and also study the statistics of $T_+$ with Monte Carlo simulations. One goal of our work was to ascertain whether the occupation time $T_+$ and the time $T_m$ at which the maximum of the process is attained are statistically equivalent. For regular Brownian motion the distributions of $T_+$ and $T_m$ coincide and are given by L\'evy's arcsine law. We show that for randomly accelerated motion the distributions of $T_+$ and $T_m$ are quite similar but not identical. This conclusion follows from the exact results for the moments of the distributions and is also consistent with our Monte Carlo simulations.

- 1. CETIC asbl - Centre d’Excellence en Technologies de l’Information et de la Communication
- 2. University of Yaoundé [Cameroun]
- 3. ENSP - Ecole Nationale Supérieure Polytechnique [Yaoundé]
- 4. Temple University [Philadelphia]
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. CEA-DEN - CEA-Direction de l'Energie Nucléaire

## On determinant representations of scalar products and form factors in the SoV approach: the XXX case

### Nikolai Kitanine

^{1}J. M. Maillet^{2}G. Niccoli^{2}Véronique Terras^{3}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49 (10), pp.104002. <10.1088/1751-8113/49/10/104002 >In the present article we study the form factors of quantum integrable lattice models solvable by the separation of variables (SoVs) method. It was recently shown that these models admit universal determinant representations for the scalar products of the so-called separate states (a class which includes in particular all the eigenstates of the transfer matrix). These results permit to obtain simple expressions for the matrix elements of local operators (form factors). However, these representations have been obtained up to now only for the completely inhomogeneous versions of the lattice models considered. In this article we give a simple algebraic procedure to rewrite the scalar products (and hence the form factors) for the SoV related models as Izergin or Slavnov type determinants. This new form leads to simple expressions for the form factors in the homogeneous and thermodynamic limits. To make the presentation of our method clear, we have chosen to explain it first for the simple case of the XXX Heisenberg chain with anti-periodic boundary conditions. We would nevertheless like to stress that the approach presented in this article applies as well to a wide range of models solved in the SoV framework.

- 1. IMB - Institut de Mathématiques de Bourgogne
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## On the algebraic area of lattice walks and the Hofstadter model

### Stephane Ouvry

^{1}Stephan Wagner^{2}Shuang Wu^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.495205We consider the generating function of the algebraic area of lattice walks, evaluated at a root of unity, and its relation to the Hofstadter model. In particular, we obtain an expression for the generating function of the n-th moments of the Hofstadter Hamiltonian in terms of a complete elliptic integral, evaluated at a rational function. This in turn gives us both exact and asymptotic formulas for these moments.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Department of Mathematics [Stellenbosch]

## On the Gap and Time Interval between the First Two Maxima of Long Continuous Time Random Walks

### Philippe Mounaix

^{1}Gregory Schehr^{2}Satya N. Majumdar^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2016, pp.013303We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval $T$ where at each time step the walker waits a random time $\tau$, before performing a jump drawn from a symmetric continuous probability distribution function (PDF) $f(\eta)$, of L\'evy index $0 < \mu \leq 2$. Our study includes the case where the waiting time PDF $\Psi(\tau)$ has a power law tail, $\Psi(\tau) \propto \tau^{-1 - \gamma}$, with $0< \gamma < 1$, such that the average time between two consecutive jumps is infinite. The random motion is sub-diffusive if $\gamma < \mu/2$ (and super-diffusive if $\gamma > \mu/2$). We investigate the joint PDF of the gap $g$ between the first two highest positions of the CTRW and the time $t$ separating these two maxima. We show that this PDF reaches a stationary limiting joint distribution $p(g,t)$ in the limit of long CTRW, $T \to \infty$. Our exact analytical results show a very rich behavior of this joint PDF in the $(\gamma, \mu)$ plane, which we study in great detail. Our main results are verified by numerical simulations. This work provides a non trivial extension to CTRWs of the recent study in the discrete time setting by Majumdar et al. (J. Stat. Mech. P09013, 2014).

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

## One step replica symmetry breaking and extreme order statistics of logarithmic REMs

### Xiangyu Cao

^{1}Yan V. Fyodorov^{2}Pierre Le Doussal^{3}*SciPost Physics*, 2016, 1, pp.011Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance ("ultraviolet", UV) limit, in terms of the biased minimal process. Our approach provides connections of the replica framework to results in the probability literature and sheds further light on the freezing/duality conjecture which was the source of many previous results for log-REMs. In this way we derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations) in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the second min statistics is largely independent of details of UV data, whose influence is seen only through the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of $1/f$-noise.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. School of Mathematical Sciences [London]
- 3. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Optical-lattice-assisted magnetic phase transition in a spin-orbit-coupled Bose-Einstein condensate

### Giovanni I. Martone

^{1, 2, 3, 4}Tomoki Ozawa^{4}Chunlei Qu^{4}Sandro Stringari^{4}*Physical Review A*, American Physical Society, 2016, 94 (4), pp.043629- 1. Università degli studi di Bari
- 2. INFN, Sezione di Bari - Istituto Nazionale di Fisica Nucleare, Sezione di Bari
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. INO-CNR BEC - Università di Trento

## Optomechanical many-body cooling using frustration

### Thomás Fogarty

^{1}Haggai Landa^{2}Cecilia Cormick^{3}Giovanna Morigi^{1}*Physical Review A*, American Physical Society, 2016, 94 (2), pp.023844- 1. Universität des Saarlandes [Saarbrücken]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IFEG - Instituto de Fisica Enrique Gaviola

## Origin of emission from square-shaped organic microlasers

### S. Bittner

^{1, 2}C. Lafargue^{2}I. Gozhyk^{2, 3}N. Djellali^{2}L. Milliet^{2}D. T. Hickox-Young^{2}C. Ulysse^{4}D. Bouche^{5}R. Dubertrand^{6}E. Bogomolny^{7}J. Zyss^{2}M. Lebental^{2}*EPL*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2016, 113, pp.54002The emission from open cavities with non-integrable features remains a challenging problem of practical as well as fundamental relevance. Square-shaped dielectric microcavities provide a favorable case study with generic implications for other polygonal resonators. We report on a joint experimental and theoretical study of square-shaped organic microlasers exhibiting a far-field emission that is strongly concentrated in the directions parallel to the side walls of the cavity. A semiclassical model for the far-field distributions is developed that is in agreement with even fine features of the experimental findings. Comparison of the model calculations with the experimental data allows the precise identification of the lasing modes and their emission mechanisms, providing strong support for a physically intuitive ray-dynamical interpretation. Special attention is paid to the role of diffraction and the finite side length.

- 1. Department of Applied Physics, Yale University
- 2. LPQM - Laboratoire de Photonique Quantique et Moléculaire
- 3. SVI - Surface du Verre et Interfaces
- 4. LPN - Laboratoire de photonique et de nanostructures
- 5. CMLA - Centre de Mathématiques et de Leurs Applications
- 6. Université de Liège
- 7. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Partial transpose criteria for symmetric states

### F. Bohnet-Waldraff

^{1, 2}D. Braun^{2}O. Giraud^{1}*Physical Review A*, American Physical Society, 2016, 94 (4), pp.042343- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Eberhard Karls Universität Tübingen

## Phase diagram of a graphene bilayer in the zero-energy Landau level

### Angelika Knothe

^{1, 2}Thierry Jolicoeur^{2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (23), pp.235149- 1. University of Freiburg [Freiburg]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

### P. Karpov

^{1}S. Brazovskii^{2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (12), pp.125108- 1. MISIS - National University of Science and Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Poisson-Boltzmann thermodynamics of counter-ions confined by curved hard walls

### Ladislav Samaj

^{1}E. Trizac^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.012601We consider a set of identical mobile point-like charges (counter-ions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively 1D plates and the 2D cylinder have already been solved, the 3D sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion/explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counter-ions inside a charged sphere (salt-free system).

- 1. Institute of Physics, Slovak Academy of Sciences
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Post-processing procedure for industrial quantum key distribution systems

### Evgeny Kiktenko

^{1}Anton Trushechkin^{2}Yury Kurochkin^{3}Aleksey Fedorov^{4, 3}*Journal of Physics: Conference Series*, IOP Publishing, 2016, 741, pp.012081- 1. Bauman Moscow State Technical University
- 2. SMI - Steklov Mathematical Institute
- 3. Russian Quantum Center
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Quantum Levy flights and multifractality of dipolar excitations in a random system

### X. Deng

^{1}B. L. Altshuler^{2, 3}G. V. Shlyapnikov^{4, 2, 5, 6, 7}L. Santos^{1}*Physical Review Letters*, American Physical Society, 2016, 117, pp.020401We consider dipolar excitations propagating via dipole-induced exchange among immobile molecules randomly spaced in a lattice. The character of the propagation is determined by long-range hops (Levy flights). We analyze the eigen-energy spectra and the multifractal structure of the wavefunctions. In 1D and 2D all states are localized, although in 2D the localization length can be extremely large leading to an effective localization-delocalization crossover in realistic systems. In 3D all eigenstates are extended but not always ergodic, and we identify the energy intervals of ergodic and non-ergodic states. The reduction of the lattice filling induces an ergodic to non-ergodic transition, and the excitations are mostly non-ergodic at low filling.

- 1. LUH - Leibniz Universität Hannover [Hannover]
- 2. Kavli Institute for Theoretical Physics
- 3. Columbia University [New York]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 6. Russian Quantum Center
- 7. Wuhan Institute of Physics and Mathematics

## Quantumness of spin-1 states

### Fabian Bohnet-Waldraff

^{1, 2}Daniel Braun^{2}Olivier Giraud^{1}*Physical Review A*, American Physical Society, 2016, 93, pp.012104We investigate quantumness of spin-1 states, defined as the Hilbert-Schmidt distance to the convex hull of spin coherent states. We derive its analytic expression in the case of pure states as a function of the smallest eigenvalue of the Bloch matrix and give explicitly the closest classical state for an arbitrary pure state. Numerical evidence is provided that the exact formula for pure states provides an upper bound on the quantumness of mixed states. Due to the connection between quantumness and entanglement we obtain new insights into the geometry of symmetric entangled states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute für Theoretische Physik

## Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model

### Silvio Franz

^{1}Giacomo Gradenigo^{2, 1, 3}Stefano Spigler^{1}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.032601We study how the thermodynamic properties of the Triangular Plaquette Model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in Kinetically Constrained Models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model Random-Diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "Random First-Order" kind. Finally, we give support to our conjectures studying the finite temperature phase diagram of the Random-Diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free-energy and configurational entropy can be computed by means of the cavity equations.

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

## Rare events statistics of random walks on networks: localization and other dynamical phase transitions

### Caterina De Bacco

^{1}Alberto Guggiola^{2}Reimer Kühn^{3}Pierre Paga^{3}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.184003Rare event statistics for random walks on complex networks are investigated using the large deviations formalism. Within this formalism, rare events are realized as typical events in a suitably deformed path-ensemble, and their statistics can be studied in terms of spectral properties of a deformed Markov transition matrix. We observe two different types of phase transition in such systems: (i) rare events which are singled out for sufficiently large values of the deformation parameter may correspond to {\em localized\/} modes of the deformed transition matrix, (ii) "mode-switching transitions" may occur as the deformation parameter is varied. Details depend on the nature of the observable for which the rare event statistics is studied, as well as on the underlying graph ensemble. In the present letter we report on the statistics of the average degree of the nodes visited along a random walk trajectory in Erd\H{o}s-R\'enyi networks. Large deviations rate functions and localization properties are studied numerically. For observables of the type considered here, we also derive an analytical approximation for the Legendre transform of the large-deviations rate function, which is valid in the large connectivity limit. It is found to agree well with simulations.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. Department of Mathematics, King's College London

## Renormalized jellium model for colloidal mixtures

### María Isabel García De Soria

^{1}Carlos E. Álvarez^{2}Emmanuel Trizac^{3}*Physical Review E*, American Physical Society (APS), 2016, 94, pp.042609- 1. Fisica Teorica, Universidad de Sevilla
- 2. Universidad del Rosario, Bogota
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Resonant pairing of excitons in semiconductor heterostructures

### S. V. Andreev

^{1, 2, 3}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (14), pp.140501 (1-5). <10.1103/PhysRevB.94.140501>We suggest indirect excitons in two-dimensional semiconductor heterostructures as a platform for the realization of a bosonic analog of the Bardeen-Cooper-Schrieffer superconductor. The quantum phase transition to a biexcitonic gapped state can be controlled in situ by tuning the electric field applied to the structure in the growth direction. The proposed playground should allow one to go to strongly correlated and high-temperature regimes, unattainable with Feshbach resonant atomic gases.

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

## Rich Polymorphic Behavior of Wigner Bilayers

### Moritz Antlanger

^{1, 2}Gerhard Kahl^{1}Martial Mazars^{2}Ladislav Šamaj^{3, 4}Emmanuel Trizac^{4}*Physical Review Letters*, American Physical Society, 2016, 117 (11), pp.118002- 1. Vienna University of Technology [Vienna]
- 2. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 3. Institute of Physics, Slovak Academy of Sciences
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Scattering on two Aharonov-Bohm vortices

### Eugene Bogomolny

^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.485202The problem of two Aharonov-Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed in [J. M. Myers, J. Math. Phys. \textbf{6}, 1839 (1963)] for diffraction on a slit can be generalized to get an explicit solution for AB vortices. Due to singular nature of AB interaction the Green function and the scattering amplitude for two AB vortices obey a series of partial differential equations. Coefficients entering these equations, in their turn, fulfill ordinary non-linear differential equations whose solutions can be obtained from a solution of the Painleve V (or III) equation. The asymptotics of necessary functions for very large and very small distances between two vortices are calculated explicitly. Taken together, it means that the problem of two AB vortices is integrable.

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

## Schrödinger approach to mean field games

### Igor Swiecicki

^{1, 2}Thierry Gobron^{1}Denis Ullmo^{2}*Physical Review Letters*, American Physical Society, 2016, 116, pp.128701Mean Field Games (MFG) provide a theoretical frame to model socio-economic systems. In this letter, we study a particular class of MFG which shows strong analogies with the {\em non-linear Schr\"odinger and Gross-Pitaevski equations} introduced in physics to describe a variety of physical phenomena ranging from deep-water waves to interacting bosons. Using this bridge many results and techniques developed along the years in the latter context can be transferred to the former. As an illustration, we study in some details an example in which the "players" in the mean field game are under a strong incentive to coordinate themselves.

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

## Spectroscopic probe of the van der Waals interaction between polar molecules and a curved surface

### Giuseppe Bimonte

^{1, 2}Thorsten Emig^{3, 4, 5}R. L. Jaffe^{6, 4}Mehran Kardar^{4}*Physical Review A*, American Physical Society, 2016, 94 (2), pp.022509- 1. Università degli studi di Napoli Federico II [Napoli]
- 2. INFN, Sezione di Napoli - Istituto Nazionale di Fisica Nucleare, Sezione di Napoli
- 3. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment
- 4. Massachussetts Institute of Technology
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. Center for Theoretical Physics and Laboratory for Nuclear Science

## Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks

### V. Avetisov

^{1, 2}A. Gorsky^{3, 4}S. Nechaev^{5, 6}O. Valba^{1, 2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.012302We have considered an equilibrium ensemble of large Erd\H{o}s-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability, $p$. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples, $\mu$. Minimizing the system energy, we see for some positive $\mu$ formation of two predominantly unicolor clusters, linked by a "string" of $N_{bw}$ black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in emergence of a wide plateau on the $N_{bw}(\mu)$-curve, which is relevant to a spinodal decomposition in 1st order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby-universes in 2D gravity. We have conjectured that observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

- 1. The Semenov Institute of Chemical Physics
- 2. Department of Applied Mathematics
- 3. IITP - Institute for Information Transmission Problems
- 4. MIPT - Moscow Institute of Physics and Technology [Moscow]
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. P. N. Lebedev Physical Institute [Moscow]

## Teleportation in an indivisible quantum system

### E. O. Kiktenko

^{1}A. K. Fedorov^{2}V. I. Man'Ko^{3, 4}*Quantum Measurements and Quantum Metrology*, 2016, 3 (1), pp.13Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.

- 1. Bauman Moscow State Technical University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MIPT - Moscow Institute of Physics and Technology [Moscow]
- 4. P. N. Lebedev Physical Institute of the Russian Academy of Sciences

## Tensor eigenvalues and entanglement of symmetric states

### F. Bohnet-Waldraff

^{1, 2}D. Braun^{2}O. Giraud^{1}*Physical Review A*, American Physical Society, 2016, 94 (4), pp.042324- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Physikalisches Institut Tübingen

## The 8-vertex model with quasi-periodic boundary conditions

### G. Niccoli

^{1}V. Terras^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.044001We study the inhomogeneous 8-vertex model (or equivalently the XYZ Heisenberg spin-1/2 chain) with all kinds of integrable quasi-periodic boundary conditions: periodic, $\sigma^x$-twisted, $\sigma^y$-twisted or $\sigma^z$-twisted. We show that in all these cases but the periodic one with an even number of sites $\mathsf{N}$, the transfer matrix of the model is related, by the vertex-IRF transformation, to the transfer matrix of the dynamical 6-vertex model with antiperiodic boundary conditions, which we have recently solved by means of Sklyanin's Separation of Variables (SOV) approach. We show moreover that, in all the twisted cases, the vertex-IRF transformation is bijective. This allows us to completely characterize, from our previous results on the antiperiodic dynamical 6-vertex model, the twisted 8-vertex transfer matrix spectrum (proving that it is simple) and eigenstates. We also consider the periodic case for $\mathsf{N}$ odd. In this case we can define two independent vertex-IRF transformations, both not bijective, and by using them we show that the 8-vertex transfer matrix spectrum is doubly degenerate, and that it can, as well as the corresponding eigenstates, also be completely characterized in terms of the spectrum and eigenstates of the dynamical 6-vertex antiperiodic transfer matrix. In all these cases we can adapt to the 8-vertex case the reformulations of the dynamical 6-vertex transfer matrix spectrum and eigenstates that had been obtained by $T$-$Q$ functional equations, where the $Q$-functions are elliptic polynomials with twist-dependent quasi-periods. Such reformulations enables one to characterize the 8-vertex transfer matrix spectrum by the solutions of some Bethe-type equations, and to rewrite the corresponding eigenstates as the multiple action of some operators on a pseudo-vacuum state, in a similar way as in the algebraic Bethe ansatz framework.

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

## The dynamics of filament assembly define cytoskeletal network morphology

### Giulia Foffano

^{1}Nicolas Levernier^{2}Martin Lenz^{1}*Nature Communications*, Nature Publishing Group, 2016, 7, pp.13827The actin cytoskeleton is a key component in the machinery of eukaryotic cells, and it selfassembles out of equilibrium into a wide variety of biologically crucial structures. While the molecular mechanisms involved are well characterized, the physical principles governing the spatial arrangement of actin filaments are not understood. Here we propose that the dynamics of actin network assembly from growing filaments results from a competition between diffusion, bundling, and steric hindrance, and is responsible for the range of observed morphologies. Our model and simulations thus predict an abrupt dynamical transition between homogeneous and strongly bundled networks as a function of the actin polymerization rate. This suggests that cells may effect dramatic changes to their internal architecture through minute modifications of their nonequilibrium dynamics. Our results are consistent with available experimental data.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

## The excitonic insulator route through a dynamical phase transition induced by an optical pulse

### Serguei Brazovskii

^{1}Natasha Kirova^{2}*Journal of Experimental and Theoretical Physics (JETP) / Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki*, MAIK Nauka/Interperiodica, 2016, 149, pp.479We consider a dynamical phase transition induced by a short optical pulse in a system prone to thermodynamical instability. We address the case of pumping to excitons whose density contributes directly to the order parameter. To describe both thermodynamic and dynamic effects on equal footing, we adopt a view of the excitonic insulator for the phase transition and suggest a formation of the Bose condensate for the pumped excitons. The work is motivated by experiments in donor-acceptor organic compounds with a neutral-ionic phase transition coupled to the spontaneous lattice dimerization and to charge transfer excitons. The double nature of the ensemble of excitons leads to an intricate time evolution, in particular to macroscopic quantum oscillations from the interference between the Bose condensate of excitons and the ground state of the excitonic insulator. The coupling of excitons and the order parameter also leads to self-trapping of their wave function, akin to self-focusing in optics. The locally enhanced density of excitons can surpass a critical value to trigger the phase transformation, even if the mean density is below the required threshold. The system is stratified in domains that evolve through dynamical phase transitions and sequences of merging.

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

## The free energy of a liquid when viewed as a population of overlapping clusters

### Pierre Ronceray

^{1}Peter Harrowell^{2}*Molecular Simulation*, Taylor & Francis, 2016, 42, pp.1149The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural fluctuations arises from the local athermal constraints imposed by the overlap of adjacent coordination shells. In the context of the recently developed Favoured Local Structure model [Soft Matt. 11, 3322 (2015)], we derive explicit expressions for the structural energy and entropy in the high temperature limit, compare this approximation with simulation data and consider the extension of this free energy to the case of spatial inhomogeneity in the distribution of local structures.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Faculty of Sciences

## The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential

### Ada Altieri

^{1, 2}Silvio Franz^{2}Giorgio Parisi^{3, 1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, 2016 (9), pp.093301- 1. SMC/INFM - Department of Physics, Sapienza University of Rome
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]

## The simplest model of jamming

### Silvio Franz

^{1}Giorgio Parisi^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2016, 49, pp.145001We study a well known machine learning model -the perceptron- as a simple model of jamming of hard objects. We exhibit two regimes: 1) a convex optimisation regime where jamming is hypostatic and non-critical. 2) a non convex optimisation regime where jamming is isostatic and critical. We characterise the critical jamming phase through exponents describing the distributions law of forces and gaps. Surprisingly we find that these exponents coincide with the corresponding ones recently computed in high dimensional hard spheres. In addition, modifying the perceptron to a random linear programming problem, we show that isostaticity is not a sufficient condition for singular force and gap distributions. For that, fragmentation of the space of solutions (replica symmetry breaking) appears to be a crucial ingredient. We hypothesise universality for a large class of non-convex constrained satisfaction problems with continuous variables.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica and INFM

## Thermalization and many-body localization in systems under dynamic nuclear polarization

### Andrea De Luca

^{1}Inés Rodríguez-Arias^{1}Markus Müller^{2, 3, 4}Alberto Rosso^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2016, 94 (1), pp.014203- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Paul Scherrer Institute
- 3. The Abdus Salam International Centre for Theoretical Physics
- 4. Unibas - University of Basel

## Time and temperature-dependent correlation function of an impurity in a one-dimensional Fermi gas as a Fredholm determinant

### O. Gamayun

^{1}Andrei G. Pronko^{2}Mikhail B. Zvonarev^{3, 4}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2016, 18, pp.045005We investigate a free one-dimensional spinless Fermi gas, and the Tonks-Girardeau gas interacting with a single impurity particle of equal mass. We obtain a Fredholm determinant representation for the time-dependent correlation function of the impurity particle. This representation is valid for an arbitrary temperature and an arbitrary repulsive or attractive impurity-gas $\delta$-function interaction potential. It includes, as particular cases, the representations obtained for zero temperature and arbitrary repulsion in [Nucl. Phys. B 892, 83 (2015)], and for arbitrary temperature and infinite repulsion in [Nucl. Phys. B 520, 594 (1998)].

- 1. INSTITUUT LORENTZ - Instituut Lorentz
- 2. Steklov Institute of Mathematics at St. Petersburg
- 3. ITMO - National Research University of Information Technologies, Mechanics and Optics [St. Petersburg]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model

### Aurélien Grabsch

^{1}Christophe Texier^{1}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2016, 116 (1), pp.17004- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Tracer diffusion coefficients in a sheared inelastic Maxwell gas

### Vicente Garzó

^{1}Emmanuel Trizac^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2016, pp.073206We study the transport properties of an impurity in a sheared granular gas, in the framework of the Boltzmann equation for inelastic Maxwell models. We investigate here the impact of a nonequilibrium phase transition found in such systems, where the tracer species carries a finite fraction of the total kinetic energy (ordered phase). To this end, the diffusion coefficients are first obtained for a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. In this situation, the set of coupled Boltzmann equations are solved by means of a Chapman-Enskog-like expansion around the (local) shear flow distributions for each species, thereby retaining all the hydrodynamic orders in the shear rate $a$. Due to the anisotropy induced by the shear flow, three tensorial quantities $D_{ij}$, $D_{p,ij}$, and $D_{T,ij}$ are required to describe the mass transport process instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled algebraic equations, which can be \emph{exactly} solved as functions of the shear rate $a$, the coefficients of restitution $\alpha_{sr}$ and the parameters of the mixture (masses and composition). Once the forms of $D_{ij}$, $D_{p,ij}$, and $D_{T,ij}$ are obtained for arbitrary mole fraction $x_1=n_1/(n_1+n_2)$ (where $n_r$ is the number density of species $r$), the tracer limit ($x_1\to 0$) is carefully considered for the above three diffusion tensors. Explicit forms for these coefficients are derived showing that their shear rate dependence is significantly affected by the order-disorder transition.

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

## Ultradilute Low-Dimensional Liquids

### D. s. Petrov

^{1}G. e. Astrakharchik^{2}*Physical Review Letters*, American Physical Society, 2016, 117 (10), pp.100401- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departament de Fisica i Enginyeria Nuclear, Campus Nord B4-B5

## Universal three-body recombination and Efimov resonances in an ultracold Li-Cs mixture

### J. Ulmanis

^{1}S. Häfner^{1}R. Pires^{1}F. Werner^{2}D. S. Petrov^{3}E. D. Kuhnle^{1}M. Weidemüller^{4, 1}*Physical Review A*, American Physical Society, 2016, 93, pp.022707We study Efimov resonances via three-body loss in an ultracold two-component gas of fermionic $^6$Li and bosonic $^{133}$Cs atoms close to a Feshbach resonance at 843~G, extending results reported previously [Pires \textit{et al.}, Phys. Rev. Lett. 112, 250404 (2014)] to temperatures around 120~nK. The experimental scheme for reaching lower temperatures is based upon compensating the gravity-induced spatial separation of the mass-imbalanced gases with bichromatic optical dipole traps. We observe the first and second excited Li-Cs-Cs Efimov resonance in the magnetic field dependence of the three-body event rate constant, in good agreement with the universal zero-range theory at finite temperature [Petrov and Werner, Phys. Rev. A 92, 022704 (2015)]. Deviations are found for the Efimov ground state, and the inelasticity parameter $\eta$ is found to be significantly larger than those for single-species systems.

- 1. Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg
- 2. LKB [Collège de France] - Laboratoire Kastler Brossel
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Hefei National Laboratory for Physical Sciences at the Microscale

## Velocity Statistics of the Nagel-Schreckenberg Model

### Nicolas Bain

^{1}Thorsten Emig^{1, 2}Franz-Joseph Ulm^{3}Michael Schreckenberg^{4}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2016, 93, pp.022305The statistics of velocities in the cellular automaton model of Nagel and Schreckenberg for traffic are studied. From numerical simulations, we obtain the probability distribution function (PDF) for vehicle velocities and the velocity-velocity (vv) correlation function. We identify the probability to find a standing vehicle as a potential order parameter that signals nicely the transition between free congested flow for sufficiently large number of velocity states. Our results for the vv correlation function resemble features of a second order phase transition. We develop a 3-body approximation that allows us to relate the PDFs for velocities and headways. Using this relation, an approximation to the velocity PDF is obtained from the headway PDF observed in simulations. We find a remarkable agreement between this approximation and the velocity PDF obtained from simulations.

- 1. Massachussetts Institute of Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Department of Civil and Environmental Engineering
- 4. Universität Duisburg-Essen [Essen]

## Wigner time delay and related concepts: Application to transport in coherent conductors

### Christophe Texier

^{1}*Physica E: Low-dimensional Systems and Nanostructures*, Elsevier, 2016, 82, pp.16 - 33- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques