# LPTMS Publications

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## A balance between membrane elasticity and polymerization energy sets the shape of spherical clathrin coats

### Mohammed Saleem

^{1}Sandrine Morlot^{1}Annika Hohendahl^{1}John Manzi^{2}Martin Lenz^{3}Aurélien Roux^{1}*Nature Communications*, [London] : Nature Pub. Group, 2015, 6, pp.6249. <10.1038/ncomms7249>In endocytosis, scaffolding is one of the mechanisms to create membrane curvature by moulding the membrane into the spherical shape of the clathrin cage. However, the impact of membrane elastic parameters on the assembly and shape of clathrin lattices has never been experimentally evaluated. Here, we show that membrane tension opposes clathrin polymerization. We reconstitute clathrin budding in vitro with giant unilamellar vesicles (GUVs), purified adaptors and clathrin. By changing the osmotic conditions, we find that clathrin coats cause extensive budding of GUVs under low membrane tension while poly-merizing into shallow pits under moderate tension. High tension fully inhibits polymerization. Theoretically, we predict the tension values for which transitions between different clathrin coat shapes occur. We measure the changes in membrane tension during clathrin poly-merization, and use our theoretical framework to estimate the polymerization energy from these data. Our results show that membrane tension controls clathrin-mediated budding by varying the membrane budding energy.

- 1. Department of Biochemistry
- 2. PCC - Physico-Chimie-Curie
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## A statistical model of intra-chromosome contact maps

### L. Nazarov

^{1}M. V. Tamm^{1, 2}S. K. Nechaev^{2, 3, 4}V. A. Avetisov^{2, 5}*Soft Matter*, Royal Society of Chemistry, 2015, pp.1019The statistical properties of intra-chromosome maps obtained by a genome-wide chromosome conformation capture method (Hi-C) are described in the framework of the hierarchical crumpling model of heteropolymer chain with quenched disorder in the primary sequence. We conjecture that the observed Hi-C maps are statistical averages over many different ways of hierarchical genome folding, and show that the existence of quenched primary structure coupled with hierarchical folding can induce the observed fine structure of intra-chromosome contact maps.

- 1. Physics Department
- 2. Department of Applied Mathematics
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. P. N. Lebedev Physical Institute
- 5. The Semenov Institute of Chemical Physics

## AGT, N-Burge partitions and W_N minimal models

### Vladimir Belavin

^{1, 2}Omar Foda^{3}Raoul Santachiara^{4}*Journal of High Energy Physics*, Springer, 2015, 10, pp.073Let ${\mathcal B}^{\, p, \, p^{\prime}, \, {\mathcal H}}_{N, n}$ be a conformal block, with $n$ consecutive channels $\chi_{\i}$, $\i = 1, \cdots, n$, in the conformal field theory $\mathcal{M}^{\, p, \, p^{\prime}}_N \! \times \! \mathcal{M}^{\mathcal{H}}$, where $\mathcal{M}^{\, p, \, p^{\prime}}_N$ is a $\mathcal{W}_N$ minimal model, generated by chiral fields of spin $1, \cdots, N$, and labeled by two co-prime integers $p$ and $p^{\prime}$, $1 < p < p^{\prime}$, while $\mathcal{M}^{\mathcal{H}}$ is a free boson conformal field theory. $\mathcal{B}^{\, p, \, p^{\prime}, \mathcal{H}}_{N, n}$ is the expectation value of vertex operators between an initial and a final state. Each vertex operator is labelled by a charge vector that lives in the weight lattice of the Lie algebra $A_{N-1}$, spanned by weight vectors $\omega_1, \cdots, \omega_{N-1}$. We restrict our attention to conformal blocks with vertex operators whose charge vectors point along $\omega_1$. The charge vectors that label the initial and final states can point in any direction. Following the $\mathcal{W}_N$ AGT correspondence, and using Nekrasov's instanton partition functions without modification, to compute $\mathcal{B}^{\, p, \, p^{\prime}, \mathcal{H}}_{N, n}$, leads to ill-defined expressions. We show that restricting the states that flow in the channels $\chi_{\i}$, $\i = 1, \cdots, n$, to states labeled by $N$ partitions that satisfy conditions that we call $N$-Burge partitions, leads to well-defined expressions that we identify with $\mathcal{B}^{\, p, \, p^{\prime}, \, \mathcal{H}}_{N, n}$. We check our identification by showing that a specific non-trivial conformal block that we compute, using the $N$-Burge conditions satisfies the expected differential equation.

- 1. IITP - Institute for Information Transmission Problems
- 2. P. N. Lebedev Physical Institute [Moscow]
- 3. University of Melbourne
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Algebraic area enclosed by random walks on a lattice

### Jean Desbois

^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2015, 48 (42), pp.425001. <10.1088/1751-8113/48/42/425001>- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Anomalous transport of impurities in inelastic Maxwell gases

### Vicente Garzó

^{1}Nagi Khalil^{2}Emmanuel Trizac^{3}*European Physical Journal E*, EDP Sciences: EPJ, 2015, 38, pp.16A mixture of dissipative hard grains generically exhibits a breakdown of kinetic energy equipartition. The undriven and thus freely cooling binary problem, in the tracer limit where the density of one species becomes minute, may exhibit an extreme form of this breakdown, with the minority species carrying a finite fraction of the total kinetic energy of the system. We investigate the fingerprint of this non-equilibrium phase transition, akin to an ordering process, on transport properties. The analysis, performed by solving the Boltzmann kinetic equation from a combination of analytical and Monte Carlo techniques, hints at the possible failure of hydrodynamics in the ordered region. As a relevant byproduct of the study, the behaviour of the second and fourth-degree velocity moments is also worked out.

- 1. Departamento de Fisica
- 2. Universidad de Sevilla [Seville]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Anticoherence of spin states with point group symmetries

### D. Baguette

^{1}F. Damanet^{1}O. Giraud^{2}J. Martin^{1}*Physical Review A*, American Physical Society, 2015, 92, pp.052333We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group symmetric sets of points. We provide three different characterizations of anticoherence, and establish a link between point symmetries, anticoherence and classes of states equivalent through stochastic local operations with classical communication (SLOCC). We then investigate in detail the case of small numbers of qubits, and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.

- 1. Institut de Physique Nucléaire, Atomique et de Spectrométrie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables

### G. Niccoli

^{1}V. Terras^{2}*Letters in Mathematical Physics*, Springer Verlag, 2015, 105, pp.989Generic inhomogeneous integrable XXZ chains with arbitrary spins are studied by means of the quantum separation of variables (SOV) method. Within this framework, a complete description of the spectrum (eigenvalues and eigenstates) of the antiperiodic transfer matrix is derived in terms of discrete systems of equations involving the inhomogeneity parameters of the model. We show here that one can reformulate this discrete SOV characterization of the spectrum in terms of functional T-Q equations of Baxter's type, hence proving the completeness of the solutions to the associated systems of Bethe-type equations. More precisely, we consider here two such reformulations. The first one is given in terms of Q-solutions, in the form of trigonometric polynomials of a given degree $N_s$, of a one-parameter family of T-Q functional equations with an extra inhomogeneous term. The second one is given in terms of Q-solutions, again in the form of trigonometric polynomials of degree $N_s$ but with double period, of Baxter's usual (i.e. without extra term) T-Q functional equation. In both cases, we prove the precise equivalence of the discrete SOV characterization of the transfer matrix spectrum with the characterization following from the consideration of the particular class of Q-solutions of the functional T-Q equation: to each transfer matrix eigenvalue corresponds exactly one such Q-solution and vice versa, and this Q-solution can be used to construct the corresponding eigenstate.

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

## Athermal analogue of sheared dense Brownian suspensions

### Martin Trulsson

^{1}Mehdi Bouzid^{2}Jorge Kurchan^{2}Eric Clément^{2}Philippe Claudin^{2}Bruno Andreotti^{2}*EPL*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2015, 111, pp.18001The rheology of dense Brownian suspensions of hard spheres is investigated numer- ically beyond the low-shear-rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time scale, both related to the normal confining pressure. This pressure-controlled approach, originally developed for granular flows, reveals a striking physical analogy between the colloidal glass transition and granular jamming.

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

## Autolocalization in a dipolar exciton system

### S. V. Andreev

^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2015, 92, pp.041117We develop the autolocalization hypothesis suggested recently in [Andreev, Phys. Rev. Lett. 110, 146401 (2013)] to explain the formation of the macroscopically ordered exciton state (MOES) in semiconductor quantum wells [L. V. Butov et al., Nature (London) 418, 751 (2002)]. We argue that the onset of a periodical localizing potential having a macroscopic spatial period is possible in the systems where in addition to long-range dipolar repulsion the excitons exhibit resonant pairing at short distances. Our theory suggests, that the central incoherent part of each condensate in the MOES may represent a novel quantum molecular phase, which was predicted and discussed theoretically several years ago in the context of resonant Bose superfluids.

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

## Blast dynamics in a dissipative gas

### Matthieu Barbier

^{1}Dario Villamaina^{2}Emmanuel Trizac^{3}*Physical Review Letters*, American Physical Society, 2015, 115, pp.214301The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution is a prototypical example of self-similarity driven by conservation laws. In dissipative media however, energy conservation is violated, yet a distinctive self-similar solution appears. It hinges on the decoupling of random and coherent motion permitted by a broad class of dissipative mechanisms. This enforces a peculiar layered structure in the shock, for which we derive the full hydrodynamic solution, validated by a microscopic approach based on Molecular Dynamics simulations. We predict and evidence a succession of temporal regimes, as well as a long-time corrugation instability, also self-similar, which disrupts the blast boundary. These generic results may apply from astrophysical systems to granular gases, and invite further cross-fertilization between microscopic and hydrodynamic approaches of shockwaves.

- 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

## Branching Brownian Motion Conditioned on Particle Numbers

### Kabir Ramola

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Chaos, Solitons and Fractals*, Elsevier, 2015, 74, pp.79We study analytically the order and gap statistics of particles at time $t$ for the one dimensional branching Brownian motion, conditioned to have a fixed number of particles at $t$. The dynamics of the process proceeds in continuous time where at each time step, every particle in the system either diffuses (with diffusion constant $D$), dies (with rate $d$) or splits into two independent particles (with rate $b$). We derive exact results for the probability distribution function of $g_k(t) = x_k(t) - x_{k+1}(t)$, the distance between successive particles, conditioned on the event that there are exactly $n$ particles in the system at a given time $t$. We show that at large times these conditional distributions become stationary $P(g_k, t \to \infty|n) = p(g_k|n)$. We show that they are characterised by an exponential tail $p(g_k|n) \sim \exp[-\sqrt{\frac{|b - d|}{2 D}} ~g_k]$ for large gaps in the subcritical ($b < d$) and supercritical ($b > d$) phases, and a power law tail $p(g_k) \sim 8\left(\frac{D}{b}\right){g_k}^{-3}$ at the critical point ($b = d$), independently of $n$ and $k$. Some of these results for the critical case were announced in a recent letter [K. Ramola, S. N. Majumdar and G. Schehr, Phys. Rev. Lett. 112, 210602 (2014)].

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

## Capacitance and charge relaxation resistance of chaotic cavities – Joint distribution of two linear statistics in the Laguerre ensemble of random matrices

### Aurélien Grabsch

^{1}Christophe Texier^{2}*Europhysics letters - EPL*, Association européenne de physique, 2015, 109, pp.50004We consider the AC transport in a quantum RC circuit made of a coherent chaotic cavity with a top gate. Within a random matrix approach, we study the joint distribution for the mesoscopic capacitance $C_\mu=(1/C+1/C_q)^{-1}$ and the charge relaxation resistance $R_q$, where $C$ is the geometric capacitance and $C_q$ the quantum capacitance. We study the limit of a large number of conducting channels $N$ with a Coulomb gas method. We obtain $\langle R_q\rangle\simeq h/(Ne^2)=R_\mathrm{dc}$ and show that the relative fluctuations are of order $1/N$ both for $C_q$ and $R_q$, with strong correlations $\langle \delta C_q\delta R_q\rangle/\sqrt{\langle \delta C_q^2\rangle\,\langle \delta R_q^2\rangle}\simeq+0.707$. The detailed analysis of large deviations involves a second order phase transition in the Coulomb gas. The two dimensional phase diagram is obtained.

- 1. ENS Cachan - École normale supérieure - Cachan
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Casimir–Polder force between anisotropic nanoparticles and gently curved surfaces

### Giuseppe Bimonte

^{1}Thorsten Emig^{2}Mehran Kardar^{3}*Physical Review D*, American Physical Society, 2015, 92, pp.025028The Casimir--Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO$_2$ and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties.

- 1. INFN, Sezione di Napoli - Istituto Nazionale di Fisica Nucleare, Sezione di Napoli
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Department of Physics

## Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers

### Kabir Ramola

^{1}Kedar Damle^{2}Deepak Dhar^{2}*Physical Review Letters*, American Physical Society, 2015, 114, pp.190601Particles with only hard-core interactions can exhibit interesting high-density phases. The cases of particles in the shape of $2\times2$ squares, and $2\times 1$ dimers on a square lattice have been studied for a long time. Here, we study the interesting and more general problem of a mixture of such dimers and squares. In the fully-packed limit of no vacancies, increasing the fraction of squares enhances the power-law columnar (stripe) order present in the pure dimer limit and eventually leads to a Kosterlitz-Thouless-type (KT) phase transition to a square-rich phase with long-range columnar order. With vacancies allowed, the entire phase boundary between this columnar ordered phase and the low-density fluid phase has continuously varying exponents and is in the Ashkin-Teller universality class. These results, which we confirm by Monte-Carlo simulations, make explicit the Ashkin-Teller nature of the density-driven transition in the $2\times 2$ hard-square gas.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Tata Institute of Fundamental Research

## Comment on « Linear wave dynamics explains observations attributed to dark-solitons in a polariton quantum fluid »

### A. Amo

^{1}J. Bloch^{1}A. Bramati^{2}I. Carusotto^{3}C. Ciuti^{4}B. Deveaud-Plédran^{5}E. Giacobino^{2}G. Grosso^{6}A. Kamchatnov^{7}Guillaume Malpuech^{8}N. Pavloff^{9}S. Pigeon^{10}D. Sanvitto^{11}D. D. Solnyshkov^{8}*Physical Review Letters*, American Physical Society, 2015, 115, pp.089401In a recent preprint (arXiv:1401.1128v1) Cilibrizzi and co-workers report experiments and simulations showing the scattering of polaritons against a localised obstacle in a semiconductor microcavity. The authors observe in the linear excitation regime the formation of density and phase patterns reminiscent of those expected in the non-linear regime from the nucleation of dark solitons. Based on this observation, they conclude that previous theoretical and experimental reports on dark solitons in a polariton system should be revised. Here we comment why the results from Cilibrizzi et al. take place in a very different regime than previous investigations on dark soliton nucleation and do not reproduce all the signatures of its rich nonlinear phenomenology. First of all, Cilibrizzi et al. consider a particular type of radial excitation that strongly determines the observed patterns, while in previous reports the excitation has a plane-wave profile. Most importantly, the nonlinear relation between phase jump, soliton width and fluid velocity, and the existence of a critical velocity with the time-dependent formation of vortex-antivortex pairs are absent in the linear regime. In previous reports about dark soliton and half-dark soliton nucleation in a polariton fluid, the distinctive dark soliton physics is supported both by theory (analytical and numerical) and experiments (both continuous wave and pulsed excitation).

- 1. LPN - Laboratoire de photonique et de nanostructures
- 2. LKB (Jussieu) - Laboratoire Kastler Brossel
- 3. INO-CNR BEC Center and Dipartimento di Fisica
- 4. MPQ - Matériaux et Phénomènes Quantiques
- 5. EPFL - Ecole Polytechnique Fédérale de Lausanne
- 6. Massachusetts Institute of Technology
- 7. Institute of Spectroscopy
- 8. Institut Pascal [Aubiere]
- 9. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 10. Queen's University Belfast [Belfast]
- 11. ISAC-CNR - ISAC-CNR Lecce Section

## Condensate formation in a zero-range process with random site capacities

### Shamik Gupta

^{1, 2, 3}Mustansir Barma^{4}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2015, pp.P07018We study the effect of quenched disorder on the zero-range process (ZRP), a system of interacting particles undergoing biased hopping on a one-dimensional periodic lattice, with the disorder entering through random capacities of sites. In the usual ZRP, sites can accommodate an arbitrary number of particles, and for a class of hopping rates and high enough density, the steady state exhibits a condensate which holds a finite fraction of the total number of particles. The sites of the disordered zero-range process considered here have finite capacities chosen randomly from the Pareto distribution. From the exact steady state measure of the model, we identify the conditions for condensate formation, in terms of parameters that involve both interactions (through the hop rates) and randomness (through the distribution of the site capacities). Our predictions are supported by results obtained from a direct numerical sampling of the steady state and from Monte Carlo simulations. Our study reveals that for a given realization of disorder, the condensate can relocate on the subset of sites with largest capacities. We also study sample-to-sample variation of the critical density required to observe condensation, and show that the corresponding distribution obeys scaling, and has a Gaussian or a Levy-stable form depending on the values of the relevant parameters.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica e Astronomia, Universit'a di Firenze
- 3. MPIPKS - Max Planck Institute für Physik Komplexer System, Dresden
- 4. Department of Theoretical Physics

## Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics

### Xiangyu Cao

^{1}Alberto Rosso^{1}Raoul Santachiara^{1}*EPL*, European Physical Society, 2015, 111, pp.16001We study scaling properties of the honeycomb fully packed loop ensemble associated with a lozenge tiling model of rough surface, when the latter is driven out of equilibrium by Kardar-Parisi-Zhang (KPZ) type dynamics. We show numerically that conformal invariance and signatures of critical percolation appear in the stationary KPZ state. In terms of the two-component Coulomb gas description of the Edwards-Wilkinson stationary state, our finding is understood as the invariance of one component under the effect of the non-linear KPZ term. On the other hand, we show a breaking of conformal invariance when the level lines of the other component are considered.

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

## Connecting local active forces to macroscopic stress in elastic media

### Pierre Ronceray

^{1}Martin Lenz^{1}*Soft Matter*, Royal Society of Chemistry, 2015, 11, pp.1597In contrast with ordinary materials, living matter drives its own motion by generating active, out-of-equilibrium internal stresses. These stresses typically originate from localized active elements embedded in an elastic medium, such as molecular motors inside the cell or contractile cells in a tissue. While many large-scale phenomenological theories of such active media have been developed, a systematic understanding of the emergence of stress from the local force-generating elements is lacking. In this paper, we present a rigorous theoretical framework to study this relationship. We show that the medium's macroscopic active stress tensor is equal to the active elements' force dipole tensor per unit volume in both continuum and discrete linear homogeneous media of arbitrary geometries. This relationship is conserved on average in the presence of disorder, but can be violated in nonlinear elastic media. Such effects can lead to either a reinforcement or an attenuation of the active stresses, giving us a glimpse of the ways in which nature might harness microscopic forces to create active materials.

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

## Convex hull of a Brownian motion in confinement

### M. Chupeau

^{1}O. Bénichou^{1}S. N. Majumdar^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 91, pp.050104We study the effect of confinement on the mean perimeter of the convex hull of a planar Brownian motion, defined as the minimum convex polygon enclosing the trajectory. We use a minimal model where an infinite reflecting wall confines the walk to its one side. We show that the mean perimeter displays a surprising minimum with respect to the starting distance to the wall and exhibits a non-analyticity for small distances. In addition, the mean span of the trajectory in a fixed direction {$\theta \in ]0,\pi/2[$}, which can be shown to yield the mean perimeter by integration over $\theta$, presents these same two characteristics. This is in striking contrast with the one dimensional case, where the mean span is an increasing analytical function. The non-monotonicity in the 2D case originates from the competition between two antagonistic effects due to the presence of the wall: reduction of the space accessible to the Brownian motion and effective repulsion.

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

## Convex Hulls of Random Walks: Large-Deviation Properties

### Gunnar Claussen

^{1}Alexander K. Hartmann^{1}Satya N. Majumdar^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 91, pp.052104We study the convex hull of the set of points visited by a two-dimensional random walker of T discrete time steps. Two natural observables that characterize the convex hull in two dimensions are its perimeter L and area A. While the mean perimeter

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

## Critical behavior in topological ensembles

### K. Bulycheva

^{1, 2}A. Gorsky^{2, 3}S. Nechaev^{4, 5}*Physical Review D*, American Physical Society, 2015, 92, pp.105006We consider the relation between three physical problems: 2D directed lattice random walks, ensembles of $T_{n,n+1}$ torus knots, and instanton ensembles in 5D SQED with one compact dimension in $\Omega$ background and with 5D Chern-Simons term at the level one. All these ensembles exhibit the critical behavior typical for the "area+length+corners" statistics of grand ensembles of 2D directed paths. Using the combinatorial description, we obtain an explicit expression of the generating function for $q$-Narayana numbers which amounts to the new critical behavior in the ensemble of $T_{n,n+1}$ torus knots and in the ensemble of instantons in 5D SQED. Depending on the number of the nontrivial fugacities, we get either the critical point, or cascade of critical lines and critical surfaces. In the 5D gauge theory the phase transition is of the 3rd order, while in the ensemble of paths and ensemble of knots it is typically of the 1st order. We also discuss the relation with the integrable models.

- 1. DPPU - Department of Physics,Princeton University
- 2. IITP - Institute for Information Transmission Problems
- 3. MIPT - Moscow Institute of Physics and Technology [Moscow]
- 4. P. N. Lebedev Physical Institute [Moscow]
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Critical Casimir Force between Inhomogeneous Boundaries

### Jerome Dubail

^{1}Raoul Santachiara^{2}Thorsten Emig^{3, 2}*EPL*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2015, 112, pp.66004To study the critical Casimir force between chemically structured boundaries immersed in a binary mixture at its demixing transition, we consider a strip of Ising spins subject to alternating fixed spin boundary conditions. The system exhibits a boundary induced phase transition as function of the relative amount of up and down boundary spins. This transition is associated with a sign change of the asymptotic force and a diverging correlation length that sets the scale for the crossover between different universal force amplitudes. Using conformal field theory and a mapping to Majorana fermions, we obtain the universal scaling function of this crossover, and the force at short distances.

- 1. IJL - Institut Jean Lamour
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Massachussetts Institute of Technology

## Criticality in the approach to failure in granular materials and amorphous solids

### Jie Lin

^{1}Thomas Gueudré^{2}Alberto Rosso^{3}Matthieu Wyart^{4}*Physical Review Letters*, American Physical Society, 2015, 115, pp.168001Failure of amorphous solids is fundamental to various phenomena, including landslides and earthquakes. Recent experiments indicate that highly plastic regions form elongated structures that are especially apparent near the maximal shear stress $\Sigma_{\max}$ where failure occurs. This observation suggested that $\Sigma_{\max}$ acts as a critical point where the length scale of those structures diverges, possibly causing macroscopic transient shear bands. Here we argue instead that the entire solid phase ($\Sigma<\Sigma_{\max}$) is critical, that plasticity always involves system-spanning events, and that their magnitude diverges at $\Sigma_{\max}$ independently of the presence of shear bands. We relate the statistics and fractal properties of these rearrangements to an exponent $\theta$ that captures the stability of the material, which is observed to vary continuously with stress, and we confirm our predictions in elastoplastic models.

- 1. Center for Soft Matter Research
- 2. DISAT - Department of Applied Science and Technology
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Institute of Theoretical Physics

## Cross-talk in host–parasite associations: What do past and recent proteomics approaches tell us?

### Chérif Chetouhi

^{1}Johan Panek^{2}Ludovic Bonhomme^{3}Hicham ElalaouiCatherine Texier^{4}Thierry Langin^{1}Charissa De BekkerSerge Urbach^{5, 6, 7}Edith Demettre^{6}Dorothée Missé^{8}Philippe Holzmuller^{9}David P. HughesAndreas Zanzoni^{10}Christine Brun^{11, 10}David G. Biron^{12}*Infection, Genetics and Evolution*, 2015, 33, pp.84 - 94. <10.1016/j.meegid.2015.04.015>A cross-talk in host-parasite associations begins when a host encounters a parasite. For many host-parasite relationships, this cross-talk has been taking place for hundreds of millions of years. The co-evolution of hosts and parasites, the familiar 'arms race' results in fascinating adaptations. Over the years, host-parasite interactions have been studied extensively from both the host and parasitic point of view. Proteomics studies have led to new insights into host-parasite cross-talk and suggest that the molecular strategies used by parasites attacking animals and plants share many similarities. Likewise, animals and plants use several common molecular tactics to counter parasite attacks. Based on proteomics surveys undertaken since the post-genomic era, a synthesis is presented on the molecular strategies used by intra- and extracellular parasites to invade and create the needed habitat for growth inside the host, as well as strategies used by hosts to counter these parasite attacks. Pitfalls in deciphering host-parasite cross-talk are also discussed. To conclude, helpful advice is given with regard to new directions that are needed to discover the generic and specific molecular strategies used by the host against parasite invasion as well as by the parasite to invade, survive, and grow inside their hosts, and to finally discover parasitic molecular signatures associated with their development.

- 1. GDEC - Génétique Diversité et Ecophysiologie des Céréales
- 2. ASCR - Czech Academy of Sciences [Prague]
- 3. SMiLES - Spectroscopie, Modélisation, Interfaces pour L'Environnement et la Santé
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Faculty of Sciences, University of Montpellier, Montpellier, France
- 6. IGF - Institut de Génomique Fonctionnelle
- 7. Functional Proteomics Platform, Institute of Functional Genomics, Montpellier, France
- 8. MIVEGEC - Laboratoire de Parasitologie-Mycologie, Montpellier
- 9. CMAEE - Contrôle des maladies animales exotiques et émergentes [Montpellier]
- 10. TAGC - Technologies avancées pour le génôme et la clinique
- 11. CNRS - Centre National de la Recherche Scientifique
- 12. UMR 6023

## Direct observation of single-electron solitons and Friedel oscillations in a quasi-one dimensional material with incommensurate charge-density waves

### Christophe Brun

^{1}Serguei Brazovskii^{2}Zhao-Zhong Wang^{3}Pierre Monceau^{4}*Physica B: Condensed Matter*, Elsevier, 2015, 460 (SI), pp.88-92. <10.1016/j.physb.2014.11.046>We have performed scanning tunneling microscopy experiments in the quasi-one dimensional charge density wave (CDW) system NbSe3, where we could image and study in detail individual solitons corresponding to the self-trapping of a single electron. Our analysis shows that the type of soliton we observed is an ``Amplitude Soliton'', characterized by a vanishing CDW amplitude at the soliton center and by a pi-shift of its phase along the chain direction. Pairs of solitons or multiple solitons were also observed. Such observations could be made only in the high-temperature COW phase. Additionally, one-dimensional Friedel oscillations around charged defects could also be imaged and are found to be superimposed to the COW. The distinction between amplitude solitons and Friedel oscillations can be made without any ambiguity. (C) 2014 Elsevier B.V. All rights reserved.

- 1. INSP - Institut des Nanosciences de Paris
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LPN - Laboratoire de photonique et de nanostructures
- 4. MagSup

## Direct summation of dipole-dipole interactions using the Wolf formalism

### Björn Stenqvist

^{1}Martin Trulsson^{2}Alexei I. Abrikosov^{3}Mikael Lund^{1}*Journal of Chemical Physics*, American Institute of Physics, 2015, 143 (1), pp.014109. <10.1063/1.4923001>- 1. Department of Theoretical Chemistry
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Department of Physical Chemistry 1

## Dynamic message-passing equations for models with unidirectional dynamics

### Andrey Y. Lokhov

^{1}Marc Mézard^{2, 1}Lenka Zdeborová^{3}*Physical Review E*, American Physical Society, 2015, 91, pp.012811Understanding and quantifying the dynamics of disordered out-of-equilibrium models is an important problem in many branches of science. Using the dynamic cavity method on time trajectories, we construct a general procedure for deriving the dynamic message-passing equations for a large class of models with unidirectional dynamics, which includes the zero-temperature random field Ising model, the susceptible-infected-recovered model, and rumor spreading models. We show that unidirectionality of the dynamics is the key ingredient that makes the problem solvable. These equations are applicable to single instances of the corresponding problems with arbitrary initial conditions, and are asymptotically exact for problems defined on locally tree-like graphs. When applied to real-world networks, they generically provide a good analytic approximation of the real dynamics.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. ENS - Ecole Normale Supérieure
- 3. IPHT - Institut de Physique Théorique (ex SPhT)

## Dynamic nuclear polarization and the paradox of Quantum Thermalization

### Andrea De Luca

^{1}Alberto Rosso^{1}*Physical Review Letters*, American Physical Society, 2015, 115, pp.080401Dynamic Nuclear Polarization (DNP) is to date the most effective technique to increase the nuclear polarization up to a factor $100,000$ opening disruptive perspectives for medical applications. In DNP, the nuclear spins are driven to an - out of equilibrium - hyperpolarized state by microwave saturation of the electron spins in interaction with them. Here we show that the electron dipolar interactions compete with the local magnetic fields resulting in two distinct dynamical phases: for strong interactions the electron spins equilibrate to an extremely low effective temperature that boosts DNP efficiency. For weak interaction this spin temperature is not defined and the polarization profile has an 'hole burning' shape characteristic of the non interacting case. The study of the many-body eigenstates reveals that these two phases are intimately related to the problem of thermalization in closed quantum systems where breaking of ergodicity is expected varying the strength of the interactions.

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

## Dynamical transition in the temporal relaxation of stochastic processes under resetting

### Satya N. Majumdar

^{1}Sanjib Sabhapandit^{2}Gregory Schehr^{1}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 91, pp.052131A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation mechanism in these systems. We show that as time progresses, an inner core region around the resetting point reaches the steady state, while the region outside the core is still transient. The boundaries of the core region grow with time as power laws at late times. Alternatively, at a fixed spatial point, the system undergoes a dynamical transition from the transient to the steady state at a characteristic space dependent timescale $t^*(x)$. We calculate analytically in several examples the large deviation function associated with this spatio-temporal fluctuation and show that generically it has a second order discontinuity at a pair of critical points characterizing the edges of the inner core. Our results are verified in the numerical simulations of several models, such as simple diffusion and fluctuating one-dimensional interfaces.

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

## Edge structure of graphene monolayers in the {\nu} = 0 quantum Hall state

### Angelika Knothe

^{1, 2}Thierry Jolicoeur^{2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2015, 92, pp.165110Monolayer graphene at neutrality in the quantum Hall regime has many competing ground states with various types of ordering. The outcome of this competition is modified by the presence of the sample boundaries. In this paper we use a Hartree-Fock treatment of the electronic correlations allowing for space-dependent ordering. The edge influence is modeled by a simple perturbative effective magnetic field in valley space. We find that all phases found in the bulk of the sample, ferromagnetic, canted antiferromagnetic, charge-density wave and Kekul$\'e$ distortion are smoothly connected to a Kekul$\'e$-distorted edge. The single-particle excitations are computed taking into account the spatial variation of the order parameters. An eventual metal-insulator transition as a function of the Zeeman energy is not simply related to the type of bulk order.

- 1. University of Freiburg [Freiburg]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Effect of Curvature and Confinement on the Casimir-Polder Interaction

### Pablo Rodriguez-Lopez

^{1}Thorsten Emig^{1}Ehsan Noruzifar^{2}Roya Zandi^{3}*Physical Review A*, American Physical Society, 2015, pp.012516Modifications of Casimir-Polder interactions due to confinement inside a cylindrical cavity and due to curvature in- and outside the cavity are studied. We consider a perfectly conducting cylindrical shell with a single particle (atom or macroscopic sphere) located next to its interior or exterior surface, or two atoms placed inside the shell. By employing the scattering approach, we obtain the particle-cavity interaction and the modification of the two-particle interaction due to the cavity. We consider both retardation and thermal effects. While for the atoms a dipole description is sufficient, for the macroscopic sphere we sum (numerically) over many multipole fluctuations to compute the interaction at short separations. In the latter limit we compare to the proximity approximation and a gradient expansion and find agreement. Our results indicate an confinement induced suppression of the force between atoms. General criteria for suppression and enhancement of Casimir interactions due to confinement are discussed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Department of Chemistry and Biochemistry
- 3. Department of Physics and Astronomy

## Effective charge of cylindrical and spherical colloids immersed in an electrolyte: the quasi-planar limit

### L. Samaj

^{1, 2}E. Trizac^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2015, 48, pp.265003We consider the non-linear Poisson-Boltzmann theory for a single cylindrical or spherical macro-ion in symmetric 1:1, together with asymmetric 1:2 and 2:1 electrolytes. We focus on the regime where $\kappa a $, the ratio of the macro-ion radius $a$ over the inverse Debye length in the bulk electrolyte, is large. Analyzing the structure of the analytical expansion emerging from a multiple scale analysis, we uncover a hidden structure for the electrostatic potential. This structure, which appears after a heuristic resummation, suggests a new and convenient expansion scheme that we present and work out in detail. We show that novel exact results can thereby be obtained, in particular pertaining to effective charge properties, in complete agreement with the direct numerical solution to the problem.

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

## Effective Langevin equations for constrained stochastic processes

### Satya N. Majumdar

^{1}Henri Orland^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2015, pp.P06039We propose a novel stochastic method to exactly generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time $t_{f}$. These paths are weighted with a probability given by the overdamped Langevin dynamics. We show how these paths can be exactly generated by a local stochastic differential equation. The method is illustrated on the generation of Brownian bridges, Brownian meanders, Brownian excursions and constrained Ornstein-Uehlenbeck processes. In addition, we show how to solve this equation in the case of a general force acting on the particle. As an example, we show how to generate constrained path joining the two minima of a double-well. Our method allows to generate statistically independent paths, and is computationally very efficient.

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

## Effects of topological constraints on globular polymers

### Maxim Imakaev

^{1}Konstantin Tchourine^{2, 1}Sergei Nechaev^{3, 4}Leonid Mirny^{1, 5}*Soft Matter*, Royal Society of Chemistry, 2015, 11, pp.665Topological constraints can affect both equilibrium and dynamic properties of polymer systems, and can play a role in the organization of chromosomes. Despite many theoretical studies, the effects of topological constraints on the equilibrium state of a single compact polymer have not been systematically studied. Here we use simulations to address this longstanding problem. We find that sufficiently long unknotted polymers differ from knotted ones in the spatial and topological states of their subchains. The unknotted globule has subchains that are mostly unknotted and form asymptotically compact $R_G(s) \sim s^{1/3}$ crumples. However, crumples display high fractal dimension of the surface $d_b = 2.8$, forming excessive contacts and interpenetrating each other. We conclude that this topologically constrained equilibrium state resembles a conjectured crumpled globule [Grosberg et al., Journal de Physique, 1988, 49, 2095], but differs from its idealized hierarchy of self-similar, isolated and compact crumples.

- 1. Department of Physics [Cambridge]
- 2. Center for Genomics and Systems Biology, New York University
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. P. N. Lebedev Physical Institute
- 5. Institute for Medical Engineering and Science, MIT

## Favoured Local Structures in Liquids and Solids: a 3D Lattice Model

### Pierre Ronceray

^{1}Peter Harrowell^{2}*Soft Matter*, Royal Society of Chemistry, 2015, 11, pp.3322We investigate the connection between the geometry of Favoured Local Structures (FLS) in liquids and the associated liquid and solid properties. We introduce a lattice spin model - the FLS model on a face-centered cubic lattice - where this geometry can be arbitrarily chosen among a discrete set of 115 possible FLS. We find crystalline groundstates for all choices of a single FLS. Sampling all possible FLS's, we identify the following trends: i) low symmetry FLS's produce larger crystal unit cells but not necessarily higher energy groundstates, ii) chiral FLS's exhibit to peculiarly poor packing properties, iii) accumulation of FLS's in supercooled liquids is linked to large crystal unit cells, and iv) low symmetry FLS's tend to find metastable structures on cooling.

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

## Finite-Temperature Free Fermions and the Kardar-Parisi-Zhang Equation at Finite Time

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Grégory Schehr^{3}*Physical Review Letters*, American Physical Society, 2015, 114 (11), pp.110402 (1-5). <10.1103/PhysRevLett.114.110402>We consider the system of $N$ one-dimensional free fermions confined by a harmonic well $V(x) = m\omega^2 {x^2}/{2}$ at finite inverse temperature $\beta = 1/T$. The average density of fermions $\rho_N(x,T)$ at position $x$ is derived. For $N \gg 1$ and $\beta \sim {\cal O}(1/N)$, $\rho_N(x,T)$ is described by a scaling function interpolating between a Gaussian at high temperature, for $\beta \ll 1/N$, and the Wigner semi-circle law at low temperature, for $\beta \gg N^{-1}$. In the latter regime, we unveil a scaling limit, for $\beta {\hbar \omega}= b N^{-1/3}$, where the fluctuations close to the edge of the support, at $x \sim \pm \sqrt{2\hbar N/(m\omega)}$, are described by a limiting kernel $K^{\rm ff}_b(s,s')$ that depends continuously on $b$ and is a generalization of the Airy kernel, found in the Gaussian Unitary Ensemble of random matrices. Remarkably, exactly the same kernel $K^{\rm ff}_b(s,s')$ arises in the exact solution of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions at finite time $t$, with the correspondence $t= b^3$.

- 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

## Frictional dynamics of viscoelastic solids driven on a rough surface

### Francois P. Landes

^{1, 2}Alberto Rosso^{2}E. A. Jagla^{3}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 92, pp.012407We study the effect of viscoelastic dynamics on the frictional properties of a (mean field) spring-block system pulled on a rough surface by an external drive. When the drive moves at constant velocity V, two dynamical regimes are observed: at fast driving, above a critical threshold Vc, the system slides at the drive velocity and displays a friction force with velocity weakening. Below Vc the steady sliding becomes unstable and a stick-slip regime sets in. In the slide-hold-slide driving protocol, a peak of the friction force appears after the hold time and its amplitude increases with the hold duration. These observations are consistent with the frictional force encoded phenomenologically in the rate-and-state equations. Our model gives a microscopical basis for such macroscopic description.

- 1. The Abdus Salam International Centre for Theoretical Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Centro Atómico Bariloche and Instituto Balseiro

## From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers

### Alexander Y. Grosberg

^{1}Sergei K. Nechaev^{1, 2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2015, 48, pp.345003We consider flexible branched polymer, with quenched branch structure, and show that its conformational entropy as a function of its gyration radius $R$, at large $R$, obeys, in the scaling sense, $\Delta S \sim R^2/(a^2L)$, with $a$ bond length (or Kuhn segment) and $L$ defined as an average spanning distance. We show that this estimate is valid up to at most the logarithmic correction for any tree. We do so by explicitly computing the largest eigenvalues of Kramers matrices for both regular and "sparse" 3-branched trees, uncovering on the way their peculiar mathematical properties.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. P. N. Lebedev Physical Institute

## Gain properties of dye-doped polymer thin films

### I. Gozhyk

^{1, 2}M. BoudreauH. Rabbani HaghighiN. Djellali^{3}S. Forget^{4}S. Chénais^{4}C. Ulysse^{2}A. Brosseau^{5}R. Pansu^{5}J.-F. AudibertS. GauvinJ. Zyss^{6}M. Lebental^{3, 7}*Biophysical Reviews and Letters*, World Scientific Publishing, 2015, 92 (21), <10.1103/PhysRevB.92.214202>- 1. Laboratoire Charles Fabry / Lasers
- 2. LPN - Laboratoire de photonique et de nanostructures
- 3. LPQM - Laboratoire de Photonique Quantique et Moléculaire
- 4. LPL - Laboratoire de Physique des Lasers
- 5. PPSM - Laboratoire de Photophysique et Photochimie Supramoléculaires et Macromoléculaires
- 6. CNET Bagneux - France Telecom, Centre National d'Etudes de Télécommunications, Laboratoire de Bagneux
- 7. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Generalized Efimov effect in one dimension

### Sergej Moroz

^{1}José P. D'Incao^{2}Dmitry S. Petrov^{3}*Physical Review Letters*, American Physical Society, 2015, 115, pp.180406We study a one-dimensional quantum problem of two particles interacting with a third one via a scale-invariant subcritically attractive inverse square potential, which can be realized, for example, in a mixture of dipoles and charges confined to one dimension. We find that above a critical mass ratio, this version of the Calogero problem exhibits the generalized Efimov effect, the emergence of discrete scale invariance manifested by a geometric series of three-body bound states with an accumulation point at zero energy.

- 1. Department of physics, University of Colorado
- 2. JILA
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Generalized transport coefficients for inelastic Maxwell mixtures under shear flow

### Vicente Garzó

^{1}Emmanuel Trizac^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 92, pp.052202The Boltzmann equation framework for inelastic Maxwell models is considered to determine the transport coefficients associated with the mass, momentum and heat fluxes of a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. The Boltzmann equation is solved by means of a Chapman-Enskog-like expansion around the (local) shear flow distributions $f_r^{(0)}$ for each species that retain all the hydrodynamic orders in the shear rate. Due to the anisotropy induced by the shear flow, tensorial quantities are required to describe the transport processes instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled equations, which can be analytically solved as functions of the shear rate $a$, the coefficients of restitution $\alpha_{rs}$ and the parameters of the mixture (masses, diameters and composition). Since the reference distribution functions $f_r^{(0)}$ apply for arbitrary values of the shear rate and are not restricted to weak dissipation, the corresponding generalized coefficients turn out to be nonlinear functions of both $a$ and $\alpha_{rs}$. The dependence of the relevant elements of the three diffusion tensors on both the shear rate and dissipation is illustrated in the tracer limit case, the results showing that the deviation of the generalized transport coefficients from their forms for vanishing shear rates is in general significant. A comparison with the previous results obtained analytically for inelastic hard spheres by using Grad's moment method is carried out showing a good agreement over a wide range of values for the coefficients of restitution. Finally, as an application of the theoretical expressions derived here for the transport coefficients, thermal diffusion segregation of an intruder immersed in a granular gas is also studied.

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

## Ground-State Statistics of Directed Polymers with heavy-tailed disorder

### Thomas Gueudré

^{1}Pierre Le Doussal^{1}Jean-Philippe Bouchaud^{2}Alberto Rosso^{3}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 91, pp.062110In this mostly numerical study, we revisit the statistical properties of the ground state of a directed polymer in a $d=1+1$ "hilly" disorder landscape, i.e. when the quenched disorder has power-law tails. When disorder is Gaussian, the polymer minimizes its total energy through a collective optimization, where the energy of each visited site only weakly contributes to the total. Conversely, a hilly landscape forces the polymer to distort and explore a larger portion of space to reach some particularly deep energy sites. As soon as the fifth moment of the disorder diverges, this mechanism radically changes the standard "KPZ" scaling behaviour of the directed polymer, and new exponents prevail. After confirming again that the Flory argument accurately predicts these exponent in the tail-dominated phase, we investigate several other statistical features of the ground state that shed light on this unusual transition and on the accuracy of the Flory argument. We underline the theoretical challenge posed by this situation, which paradoxically becomes even more acute above the upper critical dimension.

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

## High values of disorder-generated multifractals and logarithmically correlated processes

### Yan Fyodorov

^{1}Olivier Giraud^{2}*Chaos, Solitons and Fractals*, Elsevier, 2015, 74, pp.15In the introductory section of the article we give a brief account of recent insights into statistics of high and extreme values of disorder-generated multifractals following a recent work by the first author with P. Le Doussal and A. Rosso (FLR) employing a close relation between multifractality and logarithmically correlated random fields. We then substantiate some aspects of the FLR approach analytically for multifractal eigenvectors in the Ruijsenaars-Schneider ensemble (RSE) of random matrices introduced by E. Bogomolny and the second author by providing an ab initio calculation that reveals hidden logarithmic correlations at the background of the disorder-generated multifractality. In the rest we investigate numerically a few representative models of that class, including the study of the highest component of multifractal eigenvectors in the Ruijsenaars-Schneider ensemble.

- 1. School of Mathematical Sciences [London]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Impurity Green’s function of a one-dimensional Fermi-gas

### O. Gamayun

^{1, 2}A. G. Pronko^{3}M. B. Zvonarev^{4}*Nuclear Physics B*, Elsevier, 2015, pp.83We consider a one-dimensional gas of spin-1/2 fermions interacting through $\delta$-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point correlation function of the spin-down fermion. This impurity Green's function is represented in the thermodynamic limit as an integral of Fredholm determinants of integrable linear integral operators.

- 1. Bogolyubov Institute for Theoretical Physics, 14-b Metrolohichna street, Kiev 03680, Ukraine
- 2. Department of Physics, Lancaster University
- 3. Steklov Mathematical Institute
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Interaction induced decay of a heteronuclear two-atom system

### Peng Xu

^{1}Jiaheng Yang^{2, 1}Min Liu^{1}Xiaodong He^{1}Yong Zeng^{1, 2}Kunpeng Wang^{1}Jin Wang^{1, 2}D. J. Papoular^{3}G. V. Shlyapnikov^{4, 5, 1, 6}Mingsheng Zhan^{1}*Nature Communications*, Nature Publishing Group, 2015, 6, pp.7803Two-atom systems in small traps are of fundamental interest, first of all for understanding the role of interactions in degenerate cold gases and for the creation of quantum gates in quantum information processing with single-atom traps. One of the key quantities is the inelastic relaxation (decay) time when one of the atoms or both are in a higher hyperfine state. Here we measure this quantity in a heteronuclear system of $^{87}$Rb and $^{85}$Rb in a micro optical trap and demonstrate experimentally and theoretically the presence of both fast and slow relaxation processes, depending on the choice of the initial hyperfine states. The developed experimental method allows us to single out a particular relaxation process and, in this sense, our experiment is a "superclean platform" for collisional physics studies. Our results have also implications for engineering of quantum states via controlled collisions and creation of two-qubit quantum gates.

- 1. Wuhan Institute of Physics and Mathematics
- 2. University of Chinese Academy of Sciences, Beijing 100049, China
- 3. INO-CNR BEC Center and Dipartimento di Fisica
- 4. Russian Quantum Center
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. Van der Waals - Zeeman Institute

## Interference effects in the two-dimensional scattering of microcavity polaritons by an obstacle: phase dislocations and resonances

### A. M. Kamchatnov

^{1}N. Pavloff^{2}*European Physical Journal D*, EDP Sciences: EPJ, 2015, pp.32We consider interference effects within the linear description of the scattering of two-dimensional microcavity polaritons by an obstacle. The polariton wave may exhibit phase dislocations created by the interference of the incident and the scattered fields. We describe these structures within the general framework of singular optics. We also discuss another type of interference effects appearing due to the formation of (quasi)resonances in the potential of a repulsive obstacle with sharp boundaries. We discuss the relevance of our approach for the description of recent experimental results and propose a criterion for evaluating the importance of nonlinear effects.

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

## Interplay of curvature and temperature in the Casimir-Polder interaction

### Giuseppe Bimonte

^{1}Thorsten Emig^{2}*Journal of Physics: Condensed Matter*, IOP Publishing, 2015, 27, pp.214018We study the Casimir-Polder interaction at finite temperatures between a polarizable small, anisotropic particle and a non-planar surface using a derivative expansion. We obtain the leading and the next-to-leading curvature corrections to the interaction for low and high temperatures. Explicit results are provided for the retarded limit in the presence of a perfectly conducting surface.

- 1. INFN, Sezione di Napoli - Istituto Nazionale di Fisica Nucleare, Sezione di Napoli
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Invariant sums of random matrices and the onset of level repulsion

### Zdzisław Burda

^{1}Giacomo Livan^{2}Pierpaolo Vivo^{3, 4}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2015, pp.P06024Using a simple rotate-and-sum procedure, we construct and solve exactly a random matrix model with peculiar features. It is invariant under the standard symmetry groups (orthogonal and unitary) and yet the interaction between eigenvalues is not Vandermondian. The ensemble contains real symmetric or complex hermitian matrices $\mathbf{S}$ of the form $\mathbf{S}=\sum_{i=1}^M \langle \mathbf{O}_i \mathbf{D}_i\mathbf{O}_i^{\mathrm{T}}\rangle$ or $\mathbf{S}=\sum_{i=1}^M \langle \mathbf{U}_i \mathbf{D}_i\mathbf{U}_i^\dagger\rangle$ respectively. The diagonal matrices $\mathbf{D}_i=\mathrm{diag}\{\lambda_1^{(i)},\ldots,\lambda_N^{(i)}\}$ are constructed from real eigenvalues drawn independently from distributions $p^{(i)}(x)$, while the matrices $\mathbf{O}_i$ and $\mathbf{U}_i$ are all orthogonal or unitary and the average $\langle\cdot\rangle$ is performed over the respective group. While the original matrices $\mathbf{D}_i$ do not exhibit level repulsion, the resulting sum $\mathbf{S}$ develops it upon averaging over multiple $(M\geq 2)$ uncorrelated rotations. We focus on the cases where $p^{(i)}(x)$ is A.) a semicircle law, or B.) a Gaussian law for all $i=1,\ldots,M$. For the choice A, in the limit $N\to\infty$ this ensemble appears spectrally indistinguishable from the standard GOE or GUE, having same spectral density, two-point correlation function, and nearest-neighbor spacing distribution $p(s)$ after unfolding. However, working out the case $N=2$ in detail, we uncover a universal (independent of the $p^{(i)}(x)$) but different from Wigner-Dyson behavior as $s\to 0^+$. The generic interaction between eigenvalues of $\mathbf{S}$ is indeed not precisely Vandermondian, despite the rotationally invariant nature of the ensemble, and classical RMT universality is restored only asymptotically. (continue...)

- 1. Faculty of Physics and Applied Computer Science, University of Science and Technology AGH
- 2. Department of Computer Science
- 3. King's College London
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Large time zero temperature dynamics of the spherical p=2-spin model of finite size

### Yan V. Fyodorov

^{1}Anthony Perret^{2}Gregory Schehr^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2015, pp.P11017We revisit the long time dynamics of the spherical fully connected spin-glass model, i.e. the spherical $p=2$-spin model, when the number of spins $N$ is large but finite. At $T=0$ where the system is in a (trivial) spin-glass phase, and on long time scale $t \gtrsim {\cal O}{(N^{2/3})}$ we show that the behavior of physical observables, like the energy, correlation and response functions, is controlled by the density of near-extreme eigenvalues at the edge of the spectrum of the coupling matrix $J$, and are thus non self-averaging. We show that the late time decay of these observables, once averaged over the disorder, is controlled by new universal exponents which we compute exactly.

- 1. School of Mathematical Sciences [London]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Liouville theory with a central charge less than one

### Sylvain Ribault

^{1, *}Raoul Santachiara^{2}*Journal of High Energy Physics*, Springer Verlag (Germany), 2015, pp.109. <10.1007/JHEP08(2015)109>We determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always spacelike, and there is no consistent timelike Liouville theory. We also study the non-analytic conformal field theories that exist at rational values of the central charge. Our claims are supported by numerical checks of crossing symmetry. We provide Python code for computing Virasoro conformal blocks, and correlation functions in Liouville theory and (generalized) minimal models.

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

## Mean perimeter of the convex hull of a random walk in a semi-infinite medium

### M. Chupeau

^{1}O. Bénichou^{1}S. N. Majumdar^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 92, pp.022145We study various properties of the convex hull of a planar Brownian motion, defined as the minimum convex polygon enclosing the trajectory, in the presence of an infinite reflecting wall. Recently, in a Rapid Communication [Phys. Rev. E \textbf{91}, 050104(R) (2015)], we announced that the mean perimeter of the convex hull at time $t$, rescaled by $\sqrt{Dt}$, is a non-monotonous function of the initial distance to the wall. In the present article, we first give all the details of the derivation of this mean rescaled perimeter, in particular its value when starting from the wall and near the wall. We then determine the physical mechanism underlying this surprising non-monotonicity of the mean rescaled perimeter by analyzing the impact of the wall on two complementary parts of the convex hull. Finally, we provide a further quantification of the convex hull by determining the mean length of the portion of the reflecting wall visited by the Brownian motion as a function of the initial distance to the wall.

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

## Microrheology to probe non-local effects in dense granular flows

### Mehdi Bouzid

^{1}Martin Trulsson^{2}Philippe Claudin^{1}Eric Clément^{1}Bruno Andreotti^{1}*EPL (Europhysics Letters)*, 2015, 109, pp.24002A granular material is observed to flow under the Coulomb yield criterion as soon as this criterion is satisfied in a remote but contiguous region of space. We investigate this non-local effect using discrete element simulations, in a geometry similar, in spirit, to the experiment of Reddy et al. [PRL 106, 108301 (2011)]: a micro-rheometer is introduced to determine the influence of a distant shear band on the local rheological behaviour. The numerical simulations recover the dominant features of this experiment: the local shear rate is proportional to that in the shear band and decreases (roughly) exponentially with the distance to the yield conditions. The numerical results are in quantitative agreement with the predictions of the non-local rheology proposed by the present authors [PRL 111, 238301 (2013)] and derived from a gradient expansion of the rheology \mu[I]. The consequences of these findings for the dynamical mechanisms controlling non-locality are finally discussed.

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

## Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution

### Moritz Binder

^{1, 2}Thomas Barthel^{3, 2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2015, 92, pp.125119For the simulation of equilibrium states and finite-temperature response functions of strongly-correlated quantum many-body systems, we compare the efficiencies of two different approaches in the framework of the density matrix renormalization group (DMRG). The first is based on matrix product purifications. The second, more recent one, is based on so-called minimally entangled typical thermal states (METTS). For the latter, we highlight the interplay of statistical and DMRG truncation errors, discuss the use of self-averaging effects, and describe schemes for the computation of response functions. For critical as well as gapped phases of the spin-1/2 XXZ chain and the one-dimensional Bose-Hubbard model, we assess computation costs and accuracies of the two methods at different temperatures. For almost all considered cases, we find that, for the same computation cost, purifications yield more accurate results than METTS -- often by orders of magnitude. The METTS algorithm becomes more efficient only for temperatures well below the system's energy gap. The exponential growth of the computation cost in the evaluation of response functions limits the attainable timescales in both methods and we find that in this regard, METTS do not outperform purifications.

- 1. LMU - Ludwig-Maximilians-Universität [München]
- 2. Duke university [Durham]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Modelling the emergence of polarity patterns for the intercellular transport of auxin in plants

### Silvia Grigolon

^{1}Peter Sollich^{2}Olivier C. Martin^{3}*Journal of the Royal Society Interface*, Royal Society, 2015, 12, pp.20141223The hormone auxin is actively transported throughout plants via protein machineries including the dedicated transporter known as PIN. The associated transport is ordered with nearby cells driving auxin flux in similar directions. Here we provide a model of both the auxin transport and of the dynamics of cellular polarisation based on flux sensing. Our main findings are: (i) spontaneous intracellular PIN polarisation arises if PIN recycling dynamics are sufficiently non-linear, (ii) there is no need for an auxin concentration gradient, and (iii) ordered multi-cellular patterns of PIN polarisation are favored by molecular noise.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. King's College London
- 3. GQE - Génétique Quantitative et Evolution (Génétique Végétale)

## Multifractality of quantum wave functions in the presence of perturbations

### Rémy Dubertrand

^{1, 2}Ignacio Garcia-Mata^{3}Bertrand Georgeot^{1}Olivier Giraud^{4}Gabriel Lemarié^{1}John Martin^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 92 (3), pp.032914. <http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032914>. <10.1103/PhysRevE.92.032914>We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases, and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems.

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

## Nano-friction in cavity quantum electrodynamics

### T. Fogarty

^{1}C. Cormick^{2}H. Landa^{3}Vladimir M. Stojanović^{4}E. Demler^{4}Giovanna Morigi^{1}*Physical Review Letters*, American Physical Society, 2015, 115, pp.233602The dynamics of cold trapped ions in a high-finesse resonator results from the interplay between the long-range Coulomb repulsion and the cavity-induced interactions. The latter are due to multiple scatterings of laser photons inside the cavity and become relevant when the laser pump is sufficiently strong to overcome photon decay. We study the stationary states of ions coupled with a mode of a standing-wave cavity as a function of the cavity and laser parameters, when the typical length scales of the two self-organizing processes, Coulomb crystallization and photon-mediated interactions, are incommensurate. The dynamics are frustrated and in specific limiting cases can be cast in terms of the Frenkel-Kontorova model, which reproduces features of friction in one dimension. We numerically recover the sliding and pinned phases. For strong cavity nonlinearities, they are in general separated by bistable regions where superlubric and stick-slip dynamics coexist. The cavity, moreover, acts as a thermal reservoir and can cool the chain vibrations to temperatures controlled by the cavity parameters and by the ions phase. These features are imprinted in the radiation emitted by the cavity, which is readily measurable in state-of-art setups of cavity quantum electrodynamics.

- 1. Universität des Saarlandes [Saarbrücken]
- 2. IFEG - Instituto de Fisica Enrique Gaviola
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Department of Physics

## Non-local rheology in dense granular flows

### Mehdi Bouzid

^{1}Adrien Izzet^{1}Martin Trulsson^{1, 2}Eric Clément^{1}Philippe Claudin^{1}Bruno Andreotti^{1}*European Physical Journal E*, EDP Sciences: EPJ, 2015, 38, pp.125The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. [Phys. Rev. Lett \textbf{103}, 036001 (2009)] for soft matter, and adapted for granular matter by Kamrin et al. [Phys. Rev. Lett. \textbf{108}, 178301 (2012)], and the gradient expansion of the local rheology $\mu(I)$ that we have proposed [Phys. Rev. Lett. \textbf{111}, 238301 (2013)]. We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

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

## Occupation times for single-file diffusion

### Olivier Bénichou

^{1}Jean Desbois^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2015, pp.P03001We consider a file of identical Brownian particles moving on the same axis x'Ox without crossing each other. They all start from the origin O at time t = 0 and are stopped at some time t. Denoting by T the time spent on the half-line [Ox) by a given particle of the line, we establish analytical formulae for the first two moments 〈T〉 and 〈T2〉. In particular, considering the limit of an infinite number of particles, we get, for the 'middle' particle (J0 is a Bessel function). This result (and also numerical simulations) shows that the distribution of T, though being close to it, is not fully a constant one.

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

## On certain functionals of the maximum of Brownian motion and their applications

### Anthony Perret

^{1}Alain Comtet^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Journal of Statistical Physics*, Springer Verlag, 2015, 161, pp.1112We consider a Brownian motion (BM) $x(\tau)$ and its maximal value $x_{\max} = \max_{0 \leq \tau \leq t} x(\tau)$ on a fixed time interval $[0,t]$. We study functionals of the maximum of the BM, of the form ${\cal O}_{\max}(t)=\int_0^t\, V(x_{\max} - x(\tau)) {\rm d} \tau$ where $V(x)$ can be any arbitrary function and develop various analytical tools to compute their statistical properties. These tools rely in particular on (i) a "counting paths" method and (ii) a path-integral approach. In particular, we focus on the case where $V(x) = \delta(x-r)$, with $r$ a real parameter, which is relevant to study the density of near-extreme values of the BM (the so called density of states), $\rho(r,t)$, which is the local time of the BM spent at given distance $r$ from the maximum. We also provide a thorough analysis of the family of functionals ${T}_{\alpha}(t)=\int_0^t (x_{\max} - x(\tau))^\alpha \, {\rm d}\tau$, corresponding to $V(x) = x^\alpha$, with $\alpha$ real. As $\alpha$ is varied, $T_\alpha(t)$ interpolates between different interesting observables. For instance, for $\alpha =1$, $T_{\alpha = 1}(t)$ is a random variable of the "area", or "Airy", type while for $\alpha=-1/2$ it corresponds to the maximum time spent by a ballistic particle through a Brownian random potential. On the other hand, for $\alpha = -1$, it corresponds to the cost of the optimal algorithm to find the maximum of a discrete random walk, proposed by Odlyzko. We revisit here, using tools of theoretical physics, the statistical properties of this algorithm which had been studied before using probabilistic methods. Finally, we extend our methods to constrained BM, including in particular the Brownian bridge, i.e., the Brownian motion starting and ending at the origin.

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

## On predicting regulatory genes by analysis of functional networks in C. elegans

### Olga V. Valba

^{1, 2}Sergei K. Nechaev^{1, 3, 2}Mark G. Sterken^{4}L. Basten Snoek^{4}Jan E. Kammenga^{4}Olga O. Vasieva^{5}*BioData Mining*, BioMed Central, 2015, 8 (1), pp.33. <10.1186/s13040-015-0066-0>- 1. Department of Applied Mathematics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. P. N. Lebedev Physical Institute [Moscow]
- 4. Laboratory of Nematology
- 5. Institute of Integrative Biology

## Phase diagram of an extended quantum dimer model on the hexagonal lattice

### Thiago Schlittler

^{1}Thomas Barthel^{2, 3}Grégoire Misguich^{4, *}Julien Vidal^{1}Rémy Mosseri^{1}*Physical Review Letters*, American Physical Society, 2015, 115, pp.217202. <http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.115.217202>. <10.1103/PhysRevLett.115.217202>We introduce a quantum dimer model on the hexagonal lattice that, in addition to the standard three-dimer kinetic and potential terms, includes a competing potential part counting dimer-free hexagons. The zero-temperature phase diagram is studied by means of quantum Monte Carlo simulations , supplemented by variational arguments. It reveals some new crystalline phases and a cascade of transitions with rapidly changing flux (tilt in the height language). We analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that this model has the microscopic ingredients needed for the " devil's staircase " scenario [E. Fradkin et al. Phys. Rev. B 69, 224415 (2004)], and is therefore expected to produce fractal variations of the ground-state flux.

- 1. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Duke university [Durham]
- 4. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Phase Diagram of the $\nu=5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width

### Kiryl Pakrouski

^{1}Michael R. Peterson^{2}Thierry Jolicoeur^{3}Vito W. Scarola^{4}Chetan Nayak^{5, 6}Matthias Troyer^{1}*Physical Review X*, American Physical Society, 2015, 5, pp.029901Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the $\nu = 5/2$ fractional quantum Hall state. But the significant controversy surrounding the nature of the $\nu = 5/2$ state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the $\nu = 5/2$ state we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau level mixing into account to lowest-order perturbatively in $\kappa$, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate non-zero width $w$ of the quantum well and sub-band mixing. We find the ground state in both the torus and spherical geometries as a function of $\kappa$ and $w$. To sort out the non-trivial competition between candidate ground states we analyze the following 4 criteria: its overlap with trial wave functions; the magnitude of energy gaps; the sign of the expectation value of an order parameter for particle-hole symmetry breaking; and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for $\kappa < {\kappa_c}(w)$, where ${\kappa_c}(w)$ is a $w$-dependent critical value $0.6 \lesssim{\kappa_c}(w)\lesssim 1$. We observe that both Landau level mixing and non-zero width suppress the excitation gap, but Landau level mixing has a larger effect in this regard. Our findings have important implications for the identification of non-Abelian fractional quantum Hall states.

- 1. Theoretische Physik
- 2. Department of Physics and Astronomy
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Department of Physics, Virginia tech
- 5. Station Q, Microsoft Research
- 6. UCSB - Physics Department, University of California at Santa Barbara

## Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture

### D. S. Petrov

^{1}*Physical Review Letters*, American Physical Society, 2015, 115, pp.155302According to the mean-field theory a condensed Bose-Bose mixture collapses when the interspecies attraction becomes stronger than the geometrical average of the intraspecies repulsions, $g_{12}^2>g_{11} g_{22}$. We show that instead of collapsing such a mixture gets into a dilute liquid-like droplet state stabilized by quantum fluctuations thus providing a direct manifestation of beyond mean-field effects. We study various properties of the droplet and find, in particular, that in a wide range of parameters its excitation spectrum lies entirely above the particle emission threshold. The droplet thus automatically evaporates itself to zero temperature, the property potentially interesting by itself and from the viewpoint of sympathetic cooling of other systems.

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

## Quantum Signature of Analog Hawking Radiation in Momentum Space

### Denis Boiron

^{1}Fabbri Alessandro^{2}Larré Pierre-Elie^{3}Nicolas Pavloff^{4}Christoph I. Westbrook^{1}Pawel Zin^{5}*Physical Review Letters.*, 2015, 115 (2), pp.025301. <http://journals.aps.org/prl/>. <10.1103/PhysRevLett.115.025301>We consider a sonic analog of a black hole realized in the one-dimensional flow of a Bose-Einstein condensate. Our theoretical analysis demonstrates that one- and two-body momentum distributions accessible by present-day experimental techniques provide clear direct evidence (i) of the occurrence of a sonic horizon, (ii) of the associated acoustic Hawking radiation, and (iii) of the quantum nature of the Hawking process. The signature of the quantum behavior persists even at temperatures larger than the chemical potential.

- 1. Laboratoire Charles Fabry / Optique atomique
- 2. Centro Fermi - Centro Studi e Ricerche "Enrico Fermi"
- 3. Dipartimento di Fisica, Universita di Trento
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. National Center for Nuclear Research (NCBJ), Warsaw

## Quasi equilibrium construction for the long time limit of glassy dynamics

### Silvio Franz

^{1}Giorgio Parisi^{2}Federico Ricci-Tersenghi^{2}Pierfrancesco Urbani^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2015, pp.P10010In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi equilibrium description on how glassy systems explore the phase space in the slow relaxation part of their dynamics. The second one is that it gives an alternative way to obtain dynamical equations starting from a dynamical rule that is static in spirit. This provides a way to overcome the difficulties encountered in the short time part of the dynamics where current conservation must be enforced. We study this approach in detail in a prototypical mean field disordered spin system, namely the p-spin spherical model, showing how we can obtain the well known equations that describes its dynamics. Then we apply the same approach to structural glasses. We first derive a set of dynamical Ornstein-Zernike equations which are very general in nature. Finally we consider two possible closure schemes for them, namely the Hypernetted Chain approximation of liquid theory and a closure of the BBGKY hierarchy that has been recently introduced by G. Szamel. From both approaches we finally find a set of dynamical Mode-Coupling like equations that are supposed to describe the system in the long time/slow dynamics regime.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica and INFM
- 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Quasi-equilibrium in glassy dynamics: a liquid theory approach

### Silvio Franz

^{1}Giorgio Parisi^{2}Pierfrancesco Urbani^{3, 1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2015, 48, pp.19FT01We introduce a quasi-equilibrium formalism in the theory of liquids in order to obtain a set of coarse grained long time dynamical equations for the two point density correlation functions. Our scheme allows to use typical approximations devised for equilibrium to study long time glassy dynamics. We study the Hypernetted Chain (HNC) approximation and a recent closure scheme by Szamel. In both cases we get dynamical equations that have the structure of the Mode-Coupling (MCT) equations in the long time region. The HNC approach, that was so far used to get equilibrium quantities is thus generalized to a fully consistent scheme where long-time dynamic quantities can also be computed. In the context of this approximation we get an asymptotic description of both equilibrium glassy dynamics at high temperature and of aging dynamics at low temperature. The Szamel approximation on the other hand is shown to lead to the exact Mode Coupling equation of G\"otze for equilibrium dynamics. We clarify the way phase space is sampled according to MCT during dynamical relaxation.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica and INFM
- 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Radiative heat transfer in 2D Dirac materials

### Pablo Rodriguez-Lopez

^{1}Wang-Kong Tse^{2}Diego A. R. Dalvit^{2}*Journal of Physics: Condensed Matter*, Institute of Physics: Hybrid Open Access, 2015, 27, pp.214019We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. Finally, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LANL - Theorical Division

## Random matrices and entanglement entropy of trapped Fermi gases

### Pasquale Calabrese

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}*Physical Review A*, American Physical Society, 2015, pp.012303We exploit and clarify the use of random matrix theory for the calculation of the entanglement entropy of free Fermi gases. We apply this method to obtain analytic predictions for Renyi entanglement entropies of a one-dimensional gas trapped by a harmonic potential in all the relevant scaling regimes. We confirm our findings with accurate numerical calculations obtained by means of an ingenious discretisation of the reduced correlation matrix.

- 1. SISSA -- International School for Advanced Studies and INFN
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Random walk with random resetting to the maximum position

### Satya N. Majumdar

^{1}Sanjib Sabhapandit^{2}Gregory Schehr^{1}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 92, pp.052126We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with probability $(1-r)$, it undergoes symmetric random walk, i.e., it hops to one of its neighboring sites, with equal probability $(1-r)/2$. For $r=0$, it reduces to a standard random walk whose typical distance grows as $\sqrt{n}$ for large $n$. In presence of a nonzero resetting rate $0

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

## Record statistics for random walk bridges

### Claude Godreche

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2015We investigate the statistics of records in a random sequence $\{x_B(0)=0,x_B(1),\cdots, x_B(n)=x_B(0)=0\}$ of $n$ time steps. The sequence $x_B(k)$'s represents the position at step $k$ of a random walk `bridge' of $n$ steps that starts and ends at the origin. At each step, the increment of the position is a random jump drawn from a specified symmetric distribution. We study the statistics of records and record ages for such a bridge sequence, for different jump distributions. In absence of the bridge condition, i.e., for a free random walk sequence, the statistics of the number and ages of records exhibits a `strong' universality for all $n$, i.e., they are completely independent of the jump distribution as long as the distribution is continuous. We show that the presence of the bridge constraint destroys this strong `all $n$' universality. Nevertheless a `weaker' universality still remains for large $n$, where we show that the record statistics depends on the jump distributions only through a single parameter $0<\mu\le 2$, known as the L\'evy index of the walk, but are insensitive to the other details of the jump distribution. We derive the most general results (for arbitrary jump distributions) wherever possible and also present two exactly solvable cases. We present numerical simulations that verify our analytical results.

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

## Reentrant behavior of the breathing-mode-oscillation frequency in a one-dimensional Bose gas

### A. Iu. Gudyma

^{1}G. E. Astrakharchik^{2}Mikhail B. Zvonarev^{1}*Physical Review A*, American Physical Society, 2015, 92, pp.021601We calculate the breathing mode frequency $\omega$ in a one-dimensional Bose gas confined to a harmonic trap of frequency $\omega_z$. We predict Exciting temporal oscillations of the density distribution is a high-precision method for probing ultracold trapped atomic gases. Interaction effects in their many-body dynamics are particularly puzzling and counter-intuitive in one spatial dimension (1D) due to enhanced quantum correlations. We consider 1D quantum Bose gas in a parabolic trap at zero temperature and explain, analytically and numerically, how oscillation frequency depends on the number of particles, their repulsion and the trap strength. We identify the frequency with the energy difference between the ground state and a particular excited state. This way we avoided resolving the dynamical evolution of the system, simplifying the problem immensely. We find an excellent quantitative agreement of our results with the data from the Innsbruck experiment [Science 325, 1224 (2009)].

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departament de Fisica i Enginyeria Nuclear, Campus Nord B4-B5

## Relaxation of Loaded ESCRT-III Spiral Springs Drives Membrane Deformation

### Nicolas Chiaruttini

^{1}Lorena Redondo-Morata^{2}Adai Colom^{1, 2, 3}Frédéric Humbert^{1}Martin Lenz^{4, *}Simon Scheuring^{2, *}Aurélien Roux^{1, 3, *}*Cell*, Elsevier, 2015, <10.1016/j.cell.2015.10.017>13 ESCRT-III is required for lipid membrane remodeling in many cellular processes, from abscission 14 to viral budding and multi-vesicular body biogenesis. However, how ESCRT-III polymerization 15 generates membrane curvature remains debated. Here we show that Snf7, the main component 16 of ESCRT-III, polymerizes into spirals at the surface of lipid bilayers. When covering the entire 17 membrane surface, these spirals stopped growing when densely packed: they had a polygonal 18 shape, suggesting that lateral compression could deform them. We reasoned that Snf7 spirals 19 could function as spiral springs. By measuring the polymerization energy and the rigidity of Snf7 20 filaments, we showed that they were deformed while growing in a confined area. Furthermore, 21 we observed that the elastic expansion of compressed Snf7 spirals generated an area difference 22 between the two sides of the membrane and thus curvature. This spring-like activity underlies the 23 driving force by which ESCRT-III could mediate membrane deformation and fission. 24 2

- 1. Biochemistry Department - University of Geneva
- 2. Bio-AFM-Lab - BIO-AFM-LAB Bio Atomic Force Microscopy Laboratory
- 3. NCCR-Chemical Biology - Swiss National Centre for Competence in Research Programme Chemical Biology
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Reversing the Critical Casimir force by shape deformation

### G. Bimonte

^{1}T. Emig^{2, 3}M. Kardar^{4}*Physics Letters B*, Elsevier, 2015, 743, pp.138The exact critical Casimir force between periodically deformed boundaries of a 2D semi-infinite strip is obtained for conformally invariant classical systems. Only two parameters (conformal charge and scaling dimension of a boundary changing operator), along withthe solution of an electrostatic problem, determine the Casimir force, rendering the theory practically applicable to any shape and arrangement. The attraction between any two mirror symmetric objects follows directly from our general result. The possibility of purely shape induced reversal of the force, as well as occurrence of stable equilibrium points, is demonstrated for certain conformally invariant models, including the tricritical Ising model.

- 1. INFN, Sezione di Napoli - Istituto Nazionale di Fisica Nucleare, Sezione di Napoli
- 2. MSE2 - Multiscale Materials Science for Energy and Environment
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Department of Physics

## Screening like-charges in one-dimensional Coulomb systems: Exact results

### Gabriel Tellez

^{1}Emmanuel Trizac^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 92, pp.042134The possibility that like-charges can attract each other under the mediation of mobile counterions is by now well documented experimentally, numerically, and analytically. Yet, obtaining exact results is in general impossible, or restricted to some limiting cases. We work out here in detail a one dimensional model that retains the essence of the phenomena present in higher dimensional systems. The partition function is obtained explicitly, from which a wealth of relevant quantities follow, such as the effective force between the charges or the counterion profile in their vicinity. Isobaric and canonical ensembles are distinguished. The case of two equal charges screened by an arbitrary number $N$ of counterions is first studied, before the more general asymmetric situation is addressed. It is shown that the parity of $N$ plays a key role in the long range physics.

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

## Spatial Extent of Branching Brownian Motion

### Kabir Ramola

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 91, pp.042131We study the one dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost ($X_{\max}\geq 0$) and leftmost ($X_{\min} \leq 0$) visited sites up to time $t$. At each time step the existing particles in the system either diffuse (with diffusion constant $D$), die (with rate $a$) or split into two particles (with rate $b$). We focus on the regime $b \leq a$ where these two extreme values $X_{\max}$ and $X_{\min}$ are strongly correlated. We show that at large time $t$, the joint probability distribution function (PDF) of the two extreme points becomes stationary $P(X,Y,t \to \infty) \to p(X,Y)$. Our exact results for $p(X,Y)$ demonstrate that the correlation between $X_{\max}$ and $X_{\min}$ is nonzero, even in the stationary state. From this joint PDF, we compute exactly the stationary PDF $p(\zeta)$ of the (dimensionless) span $\zeta = {(X_{\max} - X_{\min})}/{\sqrt{D/b}}$, which is the distance between the rightmost and leftmost visited sites. This span distribution is characterized by a linear behavior ${p}(\zeta) \sim \frac{1}{2} \left(1 + \Delta \right) \zeta$ for small spans, with $\Delta = \left(\frac{a}{b} -1\right)$. In the critical case ($\Delta = 0$) this distribution has a non-trivial power law tail ${p}(\zeta) \sim 8 \pi \sqrt{3} /\zeta^3$ for large spans. On the other hand, in the subcritical case ($\Delta > 0$), we show that the span distribution decays exponentially as ${p}(\zeta) \sim (A^2/2) \zeta \exp \left(- \sqrt{\Delta}~\zeta\right)$ for large spans, where $A$ is a non-trivial function of $\Delta$ which we compute exactly. We show that these asymptotic behaviors carry the signatures of the correlation between $X_{\max}$ and $X_{\min}$. Finally we verify our results via direct Monte Carlo simulations.

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

## Spontaneously formed autofocusing caustics in a confined self-defocusing medium

### Michael Karpov

^{1}Thibault Congy^{2}Yonatan Sivan^{3}Victor Fleurov^{1}Nicolas Pavloff^{2}Shimshon Bar-Ad^{1}*Journal of Optical Networking*, Optical Society of America, 2015, 2 (12), pp.1053. <10.1364/OPTICA.2.001053>- 1. Raymond and Beverly Sackler School of Physics and Astronomy
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Ben Gurion University

## Stable dilute supersolid of two-dimensional dipolar bosons

### Zhen-Kai Lu

^{1}Yun Li^{2}D. S. Petrov^{3}G. V. Shlyapnikov^{4, 5, 3, 6}*Physical Review Letters*, American Physical Society, 2015, 115, pp.075303We consider two-dimensional bosonic dipoles oriented perpendicularly to the plane. On top of the usual two-body contact and long-range dipolar interactions we add a contact three-body repulsion as expected, in particular, for dipoles in the bilayer geometry with tunneling. The three-body repulsion is crucial for stabilizing the system, and we show that our model allows for stable continuous space supersolid states in the dilute regime and calculate the zero-temperature phase diagram.

- 1. Max Planck Institute für quantenoptik
- 2. Swinburne University of Technology
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Russian Quantum Center
- 5. Wuhan Institute of Physics and Mathematics
- 6. Van der Waals - Zeeman Institute

## Statistical Curse of the Second Half Rank, Eulerian numbers and Stirling numbers

### Stephane Ouvry

^{1}*Markov Processes and Related Fields*, Polymath, 2015, 21, pp.779I describe the occurence of Eulerian numbers and Stirling numbers of the second kind in the combinatorics of the Statistical Curse of the Second Half Rank problem.

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

## Statistical physics methods provide the exact solution to a long-standing problem of genetics

### Areejit Samal

^{1, 2, 3}Olivier C. Martin^{4}*Physical Review Letters*, American Physical Society, 2015, 114, pp.238101Analytic and computational methods developed within statistical physics have found applications in numerous disciplines. In this letter, we use such methods to solve a long-standing problem in statistical genetics. The problem, posed by Haldane and Waddington [J.B.S. Haldane and C.H. Waddington, Genetics 16, 357-374 (1931)], concerns so-called recombinant inbred lines (RILs) produced by repeated inbreeding. Haldane and Waddington derived the probabilities of RILs when considering 2 and 3 genes but the case of 4 or more genes has remained elusive. Our solution uses two probabilistic frameworks relatively unknown outside of physics: Glauber's formula and self-consistent equations of the Schwinger-Dyson type. Surprisingly, this combination of statistical formalisms unveils the exact probabilities of RILs for any number of genes. Extensions of the framework may have applications in population genetics and beyond.

- 1. The Abdus Salam International Centre for Theoretical Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MPI-MIS - Max Planck Institute for Mathematics in the Sciences
- 4. GQE - Génétique Quantitative et Evolution (Génétique Végétale)

## Statistics of the longest interval in renewal processes

### Claude Godreche

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2015, pp.P03014We consider renewal processes where events, which can for instance be the zero crossings of a stochastic process, occur at random epochs of time. The intervals of time between events, $\tau_{1},\tau_{2},...$, are independent and identically distributed (i.i.d.) random variables with a common density $\rho(\tau)$. Fixing the total observation time to $t$ induces a global constraint on the sum of these random intervals, which accordingly become interdependent. Here we focus on the largest interval among such a sequence on the fixed time interval $(0,t)$. Depending on how the last interval is treated, we consider three different situations, indexed by $\alpha=$ I, II and III. We investigate the distribution of the longest interval $\ell^\alpha_{\max}(t)$ and the probability $Q^\alpha(t)$ that the last interval is the longest one. We show that if $\rho(\tau)$ decays faster than $1/\tau^2$ for large $\tau$, then the full statistics of $\ell^\alpha_{\max}(t)$ is given, in the large $t$ limit, by the standard theory of extreme value statistics for i.i.d. random variables, showing in particular that the global constraint on the intervals $\tau_i$ does not play any role at large times in this case. However, if $\rho(\tau)$ exhibits heavy tails, $\rho(\tau)\sim\tau^{-1-\theta}$ for large $\tau$, with index $0 <\theta<1$, we show that the fluctuations of $\ell^\alpha_{\max}(t)/t$ are governed, in the large $t$ limit, by a stationary universal distribution which depends on both $\theta$ and $\alpha$, which we compute exactly. On the other hand, $Q^{\alpha}(t)$ is generically different from its counterpart for i.i.d. variables (both for narrow or heavy tailed distributions $\rho(\tau)$). In particular, in the case $0<\theta<1$, the large $t$ behaviour of $Q^\alpha(t)$ gives rise to universal constants (depending also on both $\theta$ and $\alpha$) which we compute exactly.

- 1. IPHT - Institut de Physique Théorique (ex SPhT)
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Statistics of two-dimensional random walks, the « cyclic sieving phenomenon » and the Hofstadter model

### Stefan Mashkevich

^{1, 2}Stéphane Ouvry^{3}Alexios Polychronakos^{4}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2015, 48, pp.405001We focus on the algebraic area probability distribution of planar random walks on a square lattice with $m_1$, $m_2$, $l_1$ and $l_2$ steps right, left, up and down. We aim, in particular, at the algebraic area generating function $Z_{m_1,m_2,l_1,l_2}(Q)$ evaluated at $Q=e^{2\i\pi\over q}$, a root of unity, when both $m_1-m_2$ and $l_1-l_2$ are multiples of $q$. In the simple case of staircase walks, a geometrical interpretation of $Z_{m,0,l,0}(e^\frac{2i\pi}{q})$ in terms of the cyclic sieving phenomenon is illustrated. Then, an expression for $Z_{m_1,m_2,l_1,l_2}(-1)$, which is relevant to the Stembridge's case, is proposed. Finally, the related problem of evaluating the n-th moments of the Hofstadter Hamiltonian in the commensurate case is addressed.

- 1. Schrodinger
- 2. Bogolyubov Institute for Theoretical Physics
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Physics Department

## SU(3) and SU(4) singlet quantum Hall states at $\nu=2/3$

### Fengcheng Wu

^{1}Inti Sodemann^{1}Allan H. Macdonald^{1}Thierry Jolicoeur^{2}*Physical Review Letters*, American Physical Society, 2015, 115, pp.166805We report on an exact diagonalization study of fractional quantum Hall states at filling factor $\nu=2/3$ in a system with a four-fold degenerate $n$=0 Landau level and SU(4) symmetric Coulomb interactions. Our investigation reveals previously unidentified SU(3) and SU(4) singlet ground states which appear at flux quantum shift 2 when a spherical geometry is employed, and lie outside the established composite-fermion or multicomponent Halperin state patterns. We evaluate the two-particle correlation functions of these states, and discuss quantum phase transitions in graphene between singlet states with different number of components as magnetic field strength is increased.

- 1. The University of Texas at Austin [Austin]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Survival probability of a Brownian motion in a planar wedge of arbitrary angle

### Marie Chupeau

^{1}Olivier Bénichou^{1}Satya N. Majumdar^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 91, pp.032106We study the survival probability and the first-passage time distribution for a Brownian motion in a planar wedge with infinite absorbing edges. We generalize existing results obtained for wedge angles of the form $\pi/n$ with $n$ a positive integer to arbitrary angles, which in particular cover the case of obtuse angles. We give explicit and simple expressions of the survival probability and the first-passage time distribution in which the difference between an arbitrary angle and a submultiple of $\pi$ is contained in three additional terms. As an application, we obtain the short time development of the survival probability in a wedge of arbitrary angle.

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

## Tensor Representation of Spin States

### O. Giraud

^{1}D. Braun^{2}D. Baguette^{3}T. Bastin^{3}J. Martin^{3}*Physical Review Letters*, American Physical Society, 2015, 114, pp.080401We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Tübingen Universität - Tübingen University
- 3. Institut de Physique Nucléaire, Atomique et de Spectrométrie

## The average number of distinct sites visited by a random walker on random graphs

### Caterina De Bacco

^{1}Satya N. Majumdar^{1}Peter Sollich^{2}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2015, 48, pp.205004We study the linear large $n$ behavior of the average number of distinct sites $S(n)$ visited by a random walker after $n$ steps on a large random graph. An expression for the graph topology dependent prefactor $B$ in $S(n) = Bn$ is proposed. We use generating function techniques to relate this prefactor to the graph adjacency matrix and then devise message-passing equations to calculate its value. Numerical simulations are performed to evaluate the agreement between the message passing predictions and random walk simulations on random graphs. Scaling with system size and average graph connectivity are also analysed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. King's College London

## The contact theorem for charged fluids: from planar to curved geometries

### Juan Pablo Mallarino

^{1}Gabriel Tellez^{1}Emmanuel Trizac^{2}*Molecular Physics*, Taylor & Francis, 2015, 113, pp.2409When a Coulombic fluid is confined between two parallel charged plates, an exact relation links the difference of ionic densities at contact with the plates, to the surface charges of these boundaries. It no longer applies when the boundaries are curved, and we work out how it generalizes when the fluid is confined between two concentric spheres (or cylinders), in two and in three space dimensions. The analysis is thus performed within the cell model picture. The generalized contact relation opens the possibility to derive new exact expressions, of particular interest in the regime of strong coulombic couplings. Some emphasis is put on cylindrical geometry, for which we discuss in depth the phenomenon of counter-ion evaporation/condensation, and obtain novel results. Good agreement is found with Monte Carlo simulation data.

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

## The critical catastrophe revisited

### Clélia De Mulatier

^{1, 2}Eric Dumonteil^{3}Alberto Rosso^{2}Andrea Zoia^{1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2015, pp.P08021The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole neutron population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the neutrons may display a wild patchiness (clustering). On the contrary, imposing a population control on the total population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time.

- 1. DM2S - Département de Modélisation des Systèmes et Structures
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. SERMA - Service des Réacteurs et de Mathématiques Appliquées

## The crossing probability for directed polymers in random media

### Andrea De Luca

^{1}Pierre Le Doussal^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2015, 92, pp.040102We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. We obtain analytical expressions for the first few moments of this probability, and compare them to a numerical simulation of a discrete model at high-temperature. From these observations, several large time properties of the non-crossing probabilities are conjectured. Extensions of our formalism to more general observables are discussed.

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

## The edge-disjoint path problem on random graphs by message-passing

### Fabrizio Altarelli

^{1, 2}Alfredo Braunstein^{3, 1, 2}Luca Dall'Asta^{1, 2}Caterina De Bacco^{4}Silvio Franz^{4}*PLoS ONE*, Public Library of Science, 2015, 10, pp.0145222We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.

- 1. DISAT - Department of Applied Science and Technology
- 2. Collegio Carlo Alberto
- 3. HuGeF - Human Genetics Foundation
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Three-body recombination in heteronuclear mixtures at finite temperature

### D. S. Petrov

^{1}F. Werner^{2}*Physical Review A*, American Physical Society, 2015, 92, pp.022704Within the universal zero-range theory, we compute the three-body recombination rate to deep molecular states for two identical bosons resonantly interacting with each other and with a third atom of another species, in the absence of weakly bound dimers. The results allow for a quantitative understanding of loss resonances at finite temperature and, combined with experimental data, can be used for testing the Efimov universality and extracting the corresponding three-body parameters in a given system. Curiously, we find that the loss rate can be dramatically enhanced by the resonant heavy-heavy interaction, even for large mass ratios where this interaction is practically irrelevant for the Efimov scaling factor. This effect is important for analysing the recent loss measurements in the Cs-Li mixture.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LKB (Jussieu) - Laboratoire Kastler Brossel

## Towards an $H$-theorem for granular gases

### M. I. García De Soria

^{1}P. Maynar^{1}S. Mischler^{2}C. Mouhot^{3}T. Rey^{4}E. Trizac^{5}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2015, pp.P11009The $H$-theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribution of the gas to evolve irreversibly towards equilibrium. As such, the theorem could not be generalized to account for dissipative systems: the conservative nature of collisions is an essential ingredient in the standard derivation. For a dissipative gas of grains, we construct here a simple functional $\mathcal H$ related to the original $H$, that can be qualified as a Lyapunov functional. It is positive, and results backed by three independent simulation approaches (a deterministic spectral method, the stochastic Direct Simulation Monte Carlo technique, and Molecular Dynamics) indicate that it is also non-increasing. Both driven and unforced cases are investigated.

- 1. Fisica Teorica, Universidad de Sevilla
- 2. CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
- 3. DPMMS/CMS
- 4. LPP - Laboratoire Paul Painlevé
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Towards an H-theorem for granular gases

### Maria Isabel Garcia de Soria

^{1}Pablo Maynar^{1}S Mischler^{2}Clément Mouhot^{3}Thomas Rey^{4, 5}Emmanuel Trizac^{6}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2015, 2015, <http://iopscience.iop.org/article/10.1088/1742-5468/2015/11/P11009>. <10.1088/1742-5468/2015/11/P11009>The H-theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribution of the gas to evolve irreversibly towards equilibrium. As such, the theorem could not be generalized to account for dissipative systems: the conservative nature of collisions is an essential ingredient in the standard derivation. For a dissipative gas of grains, we construct here a simple functional H related to the original H, that can be qualified as a Lyapunov functional. It is positive, and results backed by three independent simulation approaches (a deterministic spectral method, the stochastic Direct Simulation Monte Carlo technique, and Molecular Dynamics) indicate that it is also non-increasing. Both driven and unforced cases are investigated.

- 1. Fisica Teorica, Universidad de Sevilla
- 2. CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
- 3. DPMMS/CMS
- 4. Laboratoire de Mathématiques Paul Painlevé
- 5. RAPSODI - Reliable numerical approximations of dissipative systems
- 6. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Ultracold atoms: Boltzmann avenged

### David Guéry-Odelin

^{1}Emmanuel Trizac^{2}*Nature Physics*, Nature Publishing Group, 2015, 11 (12), pp.988. <10.1038/nphys3522>- 1. Atomes Froids (LCAR)
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Unidirectional light emission from low-index polymer microlasers

### M. SchermerS. Bittner

^{1}G. SinghC. Ulysse^{2}M. Lebental^{1, 3}J. Wiersig*Applied Physics Letters*, American Institute of Physics, 2015, 106 (10), <10.1063/1.4914498>- 1. LPQM - Laboratoire de Photonique Quantique et Moléculaire
- 2. LPN - Laboratoire de photonique et de nanostructures
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Universal ground-state properties of free fermions in a d-dimensional trap

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Grégory Schehr^{3}*EPL*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2015, 112 (6), pp.60001 (1-6). <www.epljournal.org>. <10.1209/0295-5075/112/60001>The ground-state properties of N spinless free fermions in a d-dimensional confining potential are studied. We find that any n-point correlation function has a simple determinantal structure that allows us to compute several properties exactly for large N. We show that the average density has a finite support with an edge, and near this edge the density exhibits a universal (valid for a wide class of potentials) scaling behavior for large N. The associated edge scaling function is computed exactly and generalizes to any d the edge electron gas result of Kohn and Mattsson in d = 3 (Kohn W. and Mattsson A. E., Phys. Rev. Lett., 81 (1998) 3487). In addition, we calculate the kernel (that characterizes any n-point correlation function) for large N and show that, when appropriately scaled, it depends only on dimension d, but has otherwise universal scaling forms, at the edges. The edge kernel, for higher d, generalizes the Airy kernel in one dimension, well known from the random matrix theory.

- 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

## Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution

### Silvio Franz

^{1}Giorgio Parisi^{2}Pierfrancesco Urbani^{3}Francesco Zamponi^{4}*Proceeding of the national academy of sciences*, National Academy of Sciences, 2015, 112, pp.14539We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way towards a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica and INFM
- 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681
- 4. ETH Zurich