# LPTMS Publications

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## A new dipolar potential for numerical simulations of polar fluids on the 4D hypersphere

### Jean-Michel Caillol

^{1}Martin Trulsson^{2}*The Journal of Chemical Physics*, 2014, 141, pp.124111We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions : when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all the formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.

- 1. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## A singular-potential random matrix model arising in mean-field glassy systems

### Gernot Akemann

^{1}Dario Villamaina^{2}Pierpaolo Vivo^{3}*Physical Review E*, American Physical Society, 2014, 89, pp.062146We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the loop equation with the additional constraint of vanishing trace on average. The density is generally supported on two disconnected intervals lying on the two sides of the pole. In the limit of having no pole, we recover the standard semicircle. Obtained in the planar limit, our results apply to matrices with orthogonal, unitary or symplectic symmetry alike. The orthogonal case with $m=2$ is motivated by an application to spin glass physics. In the Sherrington-Kirkpatrick mean-field model, in the paramagnetic phase and for sufficiently large systems the spin glass susceptibility is a random variable, depending on the realization of disorder. It is essentially given by a linear statistics on the eigenvalues of the coupling matrix. As such its large deviation function can be computed using standard Coulomb fluid techniques. The resulting free energy of the associated fluid precisely corresponds to the partition function of our random matrix model. Numerical simulations provide an excellent confirmation of our analytical results.

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

## A universal set of qubit quantum channels

### Daniel Braun

^{1}Olivier Giraud^{2}Ion Nechita^{1}Clement Pellegrini^{3}Marko Znidaric^{4}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47 (13), pp.135302. <10.1088/1751-8113/47/13/135302>We investigate the set of quantum channels acting on a single qubit. We provide a compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize the possible geometric forms of the pure output of the channel. We provide universal sets of quantum channels for all unital qubit channels as well as for all extremal (not necessarily unital) qubit channels, in the sense that all qubit channels in these sets can be obtained by concatenation of channels in the corresponding universal set. We also show that our universal sets are essentially minimal.

- 1. Information et Chaos Quantiques (LPT)
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IMT - Institut de Mathématiques de Toulouse
- 4. Department of Physics, Faculty of Mathematics and Physics

## Absence of a gap in the Gaffnian state

### Thierry Jolicoeur

^{1}Takahiro Mizusaki^{2}Philippe Lecheminant^{3}*Physical Review B (Condensed Matter)*, American Physical Society, 2014, 90, pp.075116We study the Gaffnian trial wavefunction proposed to describe fractional quantum Hall correlations at Bose filling factor $\nu=2/3$ and Fermi filling $\nu=2/5$. A family of Hamiltonians interpolating between a hard-core interaction for which the physics is known and a projector whose ground state is the Gaffnian is studied in detail. We give evidence for the absence of a gap by using large-scale exact diagonalizations in the spherical geometry. This is in agreement with recent arguments based on the fact that this wavefunction is constructed from a non-unitary conformal field theory. By using the cylinder geometry, we discuss in detail the nature of the underlying minimal model and we show the appearance of heterotic conformal towers in the edge energy spectrum where left and right movers are generated by distinct primary operators.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute of Natural Sciences
- 3. LPTM - Laboratoire de Physique Théorique et Modélisation

## Area distribution of two-dimensional random walks and non Hermitian Hofstadter quantum mechanics

### Sergey Matveenko

^{1, 2}Stephane Ouvry^{2}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47, pp.185001When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non hermitian Hofstadter-like quantum model where a charged particle on a square lattice coupled to a perpendicular magnetic field hopps only to the right. In the commensurate case when the magnetic flux per unit cell is rational, an exact solution of the quantum model is obtained. Periodicity on the lattice allows to relate traces of the Nth power of the Hamiltonian to probability distribution generating functions of biased walks of length N.

- 1. Landau Institute for Theoretical Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Bound states and entanglement in the excited states of quantum spin chains

### Jan Mölter

^{1}Thomas Barthel^{2, 1}Ulrich Schollwöck^{1}Vincenzo Alba^{1}*Journal of Statistical Mechanics*, 2014, pp.P10029We investigate entanglement properties of the excited states of the spin-1/2 Heisenberg (XXX) chain with isotropic antiferromagnetic interactions, by exploiting the Bethe ansatz solution of the model. We consider eigenstates obtained from both real and complex solutions ("strings") of the Bethe equations. Physically, the former are states of interacting magnons, whereas the latter contain bound states of groups of particles. We first focus on the situation with few particles in the chain. Using exact results and semiclassical arguments, we derive an upper bound S_MAX for the entanglement entropy. This exhibits an intermediate behavior between logarithmic and extensive, and it is saturated for highly-entangled states. As a function of the eigenstate energy, the entanglement entropy is organized in bands. Their number depends on the number of blocks of contiguous Bethe-Takahashi quantum numbers. In presence of bound states a significant reduction in the entanglement entropy occurs, reflecting that a group of bound particles behaves effectively as a single particle. Interestingly, the associated entanglement spectrum shows edge-related levels. At finite particle density, the semiclassical bound S_MAX becomes inaccurate. For highly-entangled states S_A\propto L_c, with L_c the chord length, signaling the crossover to extensive entanglement. Finally, we consider eigenstates containing a single pair of bound particles. No significant entanglement reduction occurs, in contrast with the few-particle case.

- 1. Department of Physics and Arnold Sommerfeld Center for Theoretical Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Calculation of multifractal dimensions in spin chains

### Y. Y. Atas

^{1}E. Bogomolny^{1}*Philosophical transactions of the Royal Society of London. Series A: Mathematical and physical sciences*, Royal Society, The, 2014, 372, pp.20120520It was demonstrated in [Phys. Rev. E 86, 021104, (2012)], that the ground-state wave functions for a large variety of one-dimensional spin-1/2 models are multifractals in the natural spin-z basis. We present here the details of analytical derivations and numerical confirmations of these results.

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

## Casimir-Polder interaction for gently curved surfaces

### Giuseppe Bimonte

^{1}Thorsten Emig^{2}Mehran Kardar^{3}*Physical Review D*, American Physical Society, 2014, 90, pp.081702We use a derivative expansion for gently curved surfaces to compute the leading and the next-to-leading curvature corrections to the Casimir-Polder interaction between a polarizable small particle and a non-planar surface. While our methods apply to any homogeneous and isotropic surface, explicit results are presented here for perfect conductors. We show that the derivative expansion of the Casimir-Polder potential follows from a resummation of its perturbative series, for small in-plane momenta. We consider the retarded, non-retarded and classical high temperature limits.

- 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

## Cauchy’s formulas for random walks in bounded domains

### Mazzolo Alain

^{1}De Mulatier Clélia^{2, 3}Zoia Andrea^{4}*Journal of Mathematical Physics*, American Institute of Physics (AIP), 2014, 55, pp.083308Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in $B$. Similar results are obtained also for the average number of collisions performed by the walker in $B$, and an extension to absorbing media is discussed.

- 1.
- 2.
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4.

## Classical Heisenberg spins with long-range interactions: relaxation to equilibrium for finite systems

### Julien Barré

^{1}Shamik Gupta^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2014, 2014 (P02017), pp.20. <10.1088/1742-5468/2014/02/P02017>Systems with long-range interactions often relax towards statistical equilibrium over timescales that diverge with N , the number of particles. A recent work [S. Gupta and D. Mukamel, J. Stat. Mech.: Theory Exp. P03015 (2011)] analyzed a model system comprising N globally coupled classical Heisenberg spins and evolving under classical spin dynamics. It was numerically shown to relax to equilibrium over a time that scales superlinearly with N . Here, we present a detailed study of the Lenard-Balescu operator that accounts at leading order for the finite-N effects driving this relaxation. We demonstrate that corrections at this order are identically zero, so that relaxation occurs over a time longer than of order N , in agreement with the reported numerical results.

- 1. JAD - Laboratoire Jean Alexandre Dieudonné
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Clustering of branching Brownian motions in confined geometries

### Zoia AndreaDumonteil EricMazzolo AlainDe Mulatier CléliaRosso Alberto

*Physical Review E*, American Physical Society, 2014, 90, pp.042118We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behaviour can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.

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

## Condensation transition in joint large deviations of linear statistics

### Juraj Szavits-Nossan

^{1}Martin R. Evans^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47, pp.455004Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states that the condensation can be understood in terms of sums of independent and identically distributed random variables: these exhibit condensation when they are conditioned to a large deviation of their sum. It is well understood that the condensation, whereby one of the random variables contributes a finite fraction to the sum, occurs only if the underlying probability distribution (modulo exponential) is heavy-tailed, i.e. decaying slower than exponential. Here we study a similar phenomenon in which condensation is exhibited for non-heavy-tailed distributions, provided random variables are additionally conditioned on a large deviation of certain linear statistics. We provide a detailed theoretical analysis explaining the phenomenon, which is supported by Monte Carlo simulations (for the case where the additional constraint is the sample variance) and demonstrated in several physical systems. Our results suggest that the condensation is a generic phenomenon that pertains to both typical and rare events.

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

## Constraint driven condensation in large fluctuations of linear statistics

### Juraj Szavits-Nossan

^{1}Martin R. Evans^{1}Satya N. Majumdar^{2}*Physical Review Letters*, American Physical Society, 2014, 112, pp.020602Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in traffic and gelation in networks. We show here that the same condensation scenario, which normally happens only if the underlying probability distribution has tails heavier than exponential, can occur for light-tailed distributions in the presence of additional constraints. We demonstrate this phenomenon on the sample variance, whose probability distribution conditioned on the particular value of the sample mean undergoes a phase transition. The transition is manifested by a change in behavior of the large deviation rate function.

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

## Counter-ions between or at asymmetrically charged walls: 2D free-fermion point

### L. Samaj

^{1, 2}E. Trizac^{1}*Journal of Statistical Physics*, Springer Verlag (Germany), 2014, 156, pp.932This work contributes to the problem of determining effective interaction between asymmetrically (likely or oppositely) charged objects whose total charge is neutralized by mobile pointlike counter-ions of the same charge, the whole system being in thermal equilibrium. The problem is formulated in two spatial dimensions with logarithmic Coulomb interactions. The charged objects correspond to two parallel lines at distance d, with fixed line charge densities. Two versions of the model are considered: the standard "unconstrained" one with particles moving freely between the lines and the "constrained" one with particles confined to the lines. We solve exactly both systems at the free-fermion coupling and compare the results for the pressure (i.e. the force between the lines per unit length of one of the lines) with the mean-field Poisson-Boltzmann solution. For the unconstrained model, the large-d asymptotic behaviour of the free-fermion pressure differs from that predicted by the mean-field theory. For the constrained model, the asymptotic pressure coincides with the attractive van der Waals-Casimir fluctuational force. For both models, there are fundamental differences between the cases of likely-charged and oppositely-charged lines, the latter case corresponding at large distances d to a capacitor.

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

## Critical dynamics and domain motion from permittivity of the electronic ferroelectric (TMTTF)2AsF6

### S. Brazovskii

^{1, 2}Pierre Monceau^{3}F. Ya. Nad^{4}*International school-conference on electronic crystals: ECRYS-2014*, Aug 2014, Cargèse, France. 460, pp.79, Physica B: Condensed MatterThe quasi one-dimensional organic conductor (TMTTF)2AsF6 shows the charge ordering transition at Tc101K to a state of the ferroelectric Mott insulator which is still well conducting. We present and interpret the experimental data on the gigantic dielectric response in the vicinity of TCO, concentrating on the frequency dependence of the inverse $1/\epsilon$ of the complex permittivity $\epsilon=\epsilon^\prime+i\epsilon^{\prime\prime}$. Surprisingly for a ferroelectric, we could closely approach the 2nd order phase transition and to deeply reach the critical dynamics of the polarization. We could analyse the critical slowing-down when approaching Tc from both sides and to extract the anomalous power law for the frequency dependence of the order parameter viscosity. Moreover, below Tc we could extract a sharp absorption feature coming from a motion of domain walls which shows up at a frequency well below the relaxation rate.

- 1. International Institute of Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MagSup
- 4. Kotelnikov Institute of Radio Engineering and Electronics

## Delocalization of weakly interacting bosons in a 1D quasiperiodic potential

### V. P. Michal

^{1}B. L. Altshuler^{2}G. V. Shlyapnikov^{1, 3, 4}*Physical Review Letters*, American Physical Society, 2014, 113, pp.045304We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) in the regime where all single-particle states are localized. We show that the interparticle interaction may lead to the many-body delocalization and we obtain the finite-temperature phase diagram. Counterintuitively, in a wide range of parameters the delocalization requires stronger cou- pling as the temperature increases. This means that the system of bosons can undergo a transition from a fluid to insulator (glass) state under heating.

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

## Dielectric Square Resonator Investigated with Microwave Experiments

### S. Bittner

^{1}E. Bogomolny^{2}B. Dietz^{3}M. Miski-Oglu^{3}A. Richter^{3}*Physical Review E*, American Physical Society, 2014, 90, pp.052909We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination of the refractive index. Measurements with different arrangements of the emitting and the receiving antennas were performed and their influence on the symmetry properties of the field distributions was investigated in detail, showing that resonances with specific symmetries can be selected purposefully. In addition, the length spectrum deduced from the measured resonance spectra and the trace formula for the dielectric square resonator are discussed in the framework of the semiclassical model.

- 1. LPQM - Laboratoire de Photonique Quantique et Moléculaire
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institut für Kernphysik

## Diffusion in periodic, correlated random forcing landscapes

### David S Dean

^{1}Shamik Gupta^{2, *}Gleb Oshanin^{3}Alberto Rosso^{2}Grégory Schehr^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2014, 47 (37), pp.372001. <10.1088/1751-8113/47/37/372001>We study the dynamics of a Brownian particle in a strongly correlated quenched random potential defined as a periodically-extended (with period $L$) finite trajectory of a fractional Brownian motion with arbitrary Hurst exponent $H \in (0,1)$. While the periodicity ensures that the ultimate long-time behavior is diffusive, the generalised Sinai potential considered here leads to a strong logarithmic confinement of particle trajectories at intermediate times. These two competing trends lead to dynamical frustration and result in a rich statistical behavior of the diffusion coefficient $D_L$: Although one has the typical value $D^{\rm typ}_L \sim \exp(-\beta L^H)$, we show via an exact analytical approach that the positive moments ($k>0$) scale like $\langle D^k_L \rangle \sim \exp{[-c' (k \beta L^{H})^{1/(1+H)}]}$, and the negative ones as $\langle D^{-k}_L \rangle \sim \exp(a' (k \beta L^{H})^2)$, $c'$ and $a'$ being numerical constants and $\beta$ the inverse temperature. These results demonstrate that $D_L$ is strongly non-self-averaging. We further show that the probability distribution of $D_L$ has a log-normal left tail and a highly singular, one-sided log-stable right tail reminiscent of a Lifshitz singularity.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

## Diffusion with resetting in arbitrary spatial dimension

### Martin R. Evans

^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47, pp.285001We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state which exhibits non-Gaussian behaviour. We then consider the presence of an absorbing target centred at the origin and compute the survival probability and mean time to absorption of the diffusive particle by the target. The mean absorption time is finite and has a minimum value at an optimal resetting rate $r^*$ which depends on dimension. Finally we consider the problem of a finite density of diffusive particles, each resetting to its own initial position. While the typical survival probability of the target at the origin decays exponentially with time regardless of spatial dimension, the average survival probability decays asymptotically as $\exp -A (\log t)^d$ where $A$ is a constant. We explain these findings using an interpretation as a renewal process and arguments invoking extreme value statistics.

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

## Domain-wall melting in ultracold boson systems with holes and spin-flip defects

### Jad C. Halimeh

^{1}Anton Wöllert^{1}Ian P. McCulloch^{2}Ulrich Schollwöck^{1}Thomas Barthel^{1, 3}*Physical Review A*, American Physical Society, 2014, 89, pp.063603Quantum magnetism is a fundamental phenomenon of nature. As of late, it has garnered a lot of interest because experiments with ultracold atomic gases in optical lattices can be used as a simulator for phenomena of magnetic systems. A paradigmatic example is the time-evolution of a domain-wall state of a spin-1/2 Heisenberg chain, the so-called domain-wall melting. The model can be implemented by having two species of bosonic atoms with unity filling and strong on-site repulsion U in an optical lattice. In this paper, we study the domain-wall melting in such a setup on the basis of the time-dependent density matrix renormalization group (tDMRG). We are particularly interested in the effects of defects that originate from an imperfect preparation of the initial state. Typical defects are holes (empty sites) and flipped spins. We show that the dominating effects of holes on observables like the spatially resolved magnetization can be taken account of by a linear combination of spatially shifted observables from the clean case. For sufficiently large $U$, further effects due to holes become negligible. In contrast, the effects of spin flips are more severe as their dynamics occur on the same time-scale as that of the domain-wall melting itself. It is hence advisable to avoid preparation schemes that are based on spin-flips.

- 1. Department of Physics and Arnold Sommerfeld Center for Theoretical Physics
- 2. Centre for Engineered Quantum Systems
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Dynamical patterns of phase transformations from self-trapping of quantum excitons

### Tianyou Yi

^{1}Natasha Kirova^{2}Serguei Brazovskii^{1}*International school-conference on electronic crystals: ECRYS-2014*, Aug 2014, Cargèse, France. 460, pp.73, Physica B: Condensed MatterPhase transitions induced by short optical pulses is a new mainstream in studies of cooperative electronic states. Its special realization in systems with neutral-ionic transformations stands out in a way that the optical pumping goes to excitons rather than to electronic bands. We present a semi-phenomenological modeling of spacio-temporal effects applicable to any system where the optical excitons are coupled to a symmetry breaking order parameter. In our scenario, after a short initial pulse of photons, a quasi-condensate of excitons appears as a macroscopic quantum state which then evolves interacting with other degrees of freedom prone to instability. This coupling leads to self-trapping of excitons; that locally enhances their density which can surpass a critical value to trigger the phase transformation, even if the mean density is below the required threshold. The system is stratified in domains which evolve through dynamical phase transitions and may persist even after the initiating excitons have recombined. We recover dynamic interplays of fields such as the excitons wave function, electronic charge transfer and polarization, lattice deformations.

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

## Dynamics and termination cost of spatially coupled mean-field models

### Francesco Caltagirone

^{1}Silvio Franz^{2}Richard Morris^{1}Lenka Zdeborová^{1}*Physical Review E*, American Physical Society, 2014, 89, pp.012102This work is motivated by recent progress in information theory and signal processing where the so-called 'spatially coupled' design of systems leads to considerably better performance. We address relevant open questions about spatially coupled systems through the study of a simple Ising model. In particular, we consider a chain of Curie-Weiss models that are coupled by interactions up to a certain range. Indeed, it is well known that the pure (uncoupled) Curie-Weiss model undergoes a first order phase transition driven by the magnetic field, and furthermore, in the spinodal region such systems are unable to reach equilibrium in sub-exponential time if initialized in the metastable state. By contrast, the spatially coupled system is, instead, able to reach the equilibrium even when initialized to the metastable state. The equilibrium phase propagates along the chain in the form of a travelling wave. Here we study the speed of the wave-front and the so-called 'termination cost'--- \textit{i.e.}, the conditions necessary for the propagation to occur. We reach several interesting conclusions about optimization of the speed and the cost.

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

## Elastic Multi-Body Interactions on a Lattice

### D. S. Petrov

^{1}*Physical Review A*, American Physical Society, 2014, 90, pp.021601We show that by coupling two hyperfine states of an atom in an optical lattice one can independently control two-, three-, and four-body on-site interactions in a non-perturbative manner. In particular, under typical conditions of current experiments one can have a purely three- or four-body interacting gas of $^{39}$K atoms characterized by on-site interaction shifts of several 100Hz.

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

## Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings

### Arkady Pikovsky

^{1, 2}Shamik Gupta^{3}Tarcisio N. Teles^{4}Fernanda P. C. Benetti^{4}Renato Pakter^{4}Yan Levin^{4}Stefano Ruffo^{5}*Physical Review E*, American Physical Society, 2014, pp.062141We explore ensemble inequivalence in long-range interacting systems by studying an XY model of classical spins with ferromagnetic and nematic coupling. We demonstrate the inequivalence by mapping the microcanonical phase diagram onto the canonical one, and also by doing the inverse mapping. We show that the equilibrium phase diagrams within the two ensembles strongly disagree within the regions of first-order transitions, exhibiting interesting features like temperature jumps. In particular, we discuss the coexistence and forbidden regions of different macroscopic states in both the phase diagrams.

- 1. UNIPOTSDAM - Department of Physics and Astronomie, Univ. Potsdam
- 2. Department of Control Theory
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. IFUFRGS - Instituto de Física
- 5. Dipartimento di Fisica e Astronomia and CSDC

## Entanglement Generation Using Discrete Solitons in Coulomb Crystals

### H. Landa

^{1, 2}A. Retzker^{3}T. Schaetz^{4}B. Reznik^{1}*Physical Review Letters*, American Physical Society, 2014, 113, pp.053001Laser cooled and trapped ions can crystallize and feature discrete solitons, that are nonlinear, topologically-protected configurations of the Coulomb crystal. Such solitons, as their continuum counterparts, can move within the crystal, while their discreteness leads to the existence of a gap-separated, spatially-localized motional mode of oscillation above the spectrum. Suggesting that these unique properties of discrete solitons can be used for generating entanglement between different sites of the crystal, we study a detailed proposal in the context of state-of-the-art experimental techniques. We analyze the interaction of periodically-driven planar ion crystals with optical forces, revealing the effects of micromotion in radio-frequency traps inherent to such structures, as opposed to linear ion chains. The proposed method requires Doppler cooling of the crystal and sideband cooling of the soliton's localized modes alone. Since the gap separation of the latter is nearly independent of the crystal size, this approach could be particularly useful for producing entanglement and studying system-environment interactions in large, two- and possibly three-dimensional systems.

- 1. Raymond and Beverly Sackler Faculty of Exact Sciences
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. HUJ - Hebrew University of Jerusalem
- 4. University of Freiburg [Freiburg]

## Exact non-equilibrium solutions of the Boltzmann equation under a time-dependent external force

### David Guéry-Odelin

^{1}J. G. Muga^{2, 3}M. J. Ruiz-Montero^{4}E. Trizac^{5}*Physical Review Letters*, American Physical Society, 2014, 112, pp.180602We construct a novel class of exact solutions to the Boltzmann equation, in both its classical and quantum formulation, for arbitrary collision laws. When the system is subjected to a specific external forcing, the precise form of which is worked out, non equilibrium damping-less solutions are admissible. They do not contradict the $H$-theorem, but are constructed from its requirements. Interestingly, these solutions hold for time-dependent confinement. We exploit them, in a reverse-engineering perspective, to work out a protocol that shortcuts any adiabatic transformation between two equilibrium states in an arbitrarily short time-span, for an interacting system. Particle simulations of the direct Monte Carlo type fully corroborate the analytical predictions.

- 1. Atomes Froids (LCAR)
- 2. Departamento de Qumica-Fsica, UPV-EHU
- 3. Department of Physics, Shanghai University
- 4. Fisica Teorica, Universidad de Sevilla
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Excitonic Mechanism of Local Phase Transformations by Optical Pumping

### Serguei Brazovskii

^{1}Natasha Kirova^{2}*Journal of Superconductivity and Novel Magnetism*, Springer Verlag (Germany), 2014, 27, pp.1009 - 1013. <10.1007/s10948-013-2432-9>Transformations of cooperative electronic states by impacts of optical pumping or/and electrostatic doping is a new mainstream in physics of correlated systems. Here we present a semi-phenomenological modelling of spacio-temporal effects in a system where the light absorption goes through a channel creating the excitons – intra-molecular ones or bound electron-hole pairs -and finally the condensate of optical excitons feeds and stimulates phase transformations. Interacting with a near-critical order parameter and deformations, the excitons are subject to self-trapping. That locally enhances their density which can surpass a critical value to trigger the phase transformation, even if the mean density is below the required threshold. The model can be used e.g. as a simplified version of optically induced neutral-ionic transitions in organic chain compounds.

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

## Experimental and theoretical investigation of angular dependence of the Casimir force between sinusoidally corrugated surfaces

### A. A. Banishev

^{1}J. Wagner^{1}T. Emig^{2}R. Zandi^{1}U. Mohideen^{1}*Physical Review B (Condensed Matter)*, American Physical Society, 2014, 89, pp.235436In the current work we present the complete results for the measurement of normal Casimir force between shallow and smooth sinusoidally corrugated gold coated sphere and a plate at various angles between the corrugations using an atomic force microscope. All measured data were compared with the theoretical approach using the proximity force approximation and theory based on derivative expansion. In both cases real material properties of the surfaces and non-zero temperature were taken into account. Special attention is paid to the description of electrostatic interactions between corrugated surfaces at different angels between corrugations and samples reparation and characterization. The measured forces are found to be in good agreement with the theory including correlation effects of geometry and material properties and deviate significantly from the predictions of the proximity force approximation approach. This provides the quantitative confirmation for the observation of diffraction-type effects that are disregarded within the PFA approach. The obtained results open new opportunities for control of the Casimir effect in micromechanical systems.

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

## First order transition for the optimal search time of Lévy flights with resetting

### Lukasz Kusmierz

^{1, 2}Satya N. Majumdar^{3}Sanjib Sabhapandit^{4}Gregory Schehr^{3}*Physical Review Letters*, American Physical Society, 2014, 113, pp.220602We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at $x_0\geq0$, where successive jumps are drawn independently from an arbitrary jump distribution $f(\eta)$. In addition, with a probability $0\leq r \leq1$ the position of the searcher is reset to its initial position $x_0$. The efficiency of the search strategy is characterized by the mean time to find the target, i.e., the mean first passage time (MFPT) to the origin. For arbitrary jump distribution $f(\eta)$, initial position $x_0$ and resetting probability $r$, we compute analytically the MFPT. For the heavy-tailed L\'evy stable jump distribution characterized by the L\'evy index $0<\mu < 2$, we show that, for any given $x_0$, the MFPT has a global minimum in the $(\mu,r)$ plane at $(\mu^*(x_0),r^*(x_0))$. We find a remarkable first-order phase transition as $x_0$ crosses a critical value $x_0^*$ at which the optimal parameters change discontinuously. Our analytical results are in good agreement with numerical simulations.

- 1. Institute of Physics of Krakow
- 2. Department of Automatics and Biomedical Engineering
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Raman Research Institute

## Fluctuating interfaces subject to stochastic resetting

### Shamik Gupta

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Physical Review Letters*, American Physical Society, 2014, 112, pp.220601We study one-dimensional fluctuating interfaces of length $L$ where the interface stochastically resets to a fixed initial profile at a constant rate $r$. For finite $r$ in the limit $L \to \infty$, the system settles into a nonequilibrium stationary state with non-Gaussian interface fluctuations, which we characterize analytically for the Kardar-Parisi-Zhang and Edwards-Wilkinson universality class. Our results are corroborated by numerical simulations. We also discuss the generality of our results for a fluctuating interface in a generic universality class.

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

## Fluctuations in partitioning systems with few degrees of freedom

### L. Cerino

^{1}G. Gradenigo^{2, 3}A. Sarracino^{2, 4, 5}D. Villamaina^{2}A. Vulpiani^{6, 7}*Physical Review E*, American Physical Society, 2014, 89, pp.042105We study the behavior of a moving wall in contact with a particle gas and subjected to an external force. We compare the fluctuations of the system observed in the microcanonical and canonical ensembles, at varying the number of particles. Static and dynamic correlations signal significant differences between the two ensembles. Furthermore, velocity-velocity correlations of the moving wall present a complex two-time relaxation which cannot be reproduced by a standard Langevin-like description. Quite remarkably, increasing the number of gas particles in an elongated geometry, we find a typical timescale, related to the interaction between the partitioning wall and the particles, which grows macroscopically.

- 1. Dipartimento di Fisica [Rome]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. CEA - CEA Saclay
- 4. Dipartimento di Fisica
- 5. Kavli Institute for Theoretical Physics China
- 6. INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]
- 7. Kavli Institute for Theoretical Physics China,

## Fluctuations of random matrix products and 1D Dirac equation with random mass

### Kabir Ramola

^{1}Christophe Texier^{1}*Journal of Statistical Physics*, Springer Verlag (Germany), 2014, 157, pp.497-514We study the fluctuations of certain random matrix products $\Pi_N=M_N\cdots M_2M_1$ of $\mathrm{SL}(2,\mathbb{R})$, describing localisation properties of the one-dimensional Dirac equation with random mass. In the continuum limit, i.e. when matrices $M_n$'s are close to the identity matrix, we obtain convenient integral representations for the variance $\Gamma_2=\lim_{N\to\infty}\mathrm{Var}(\ln||\Pi_N||)/N$. The case studied exhibits a saturation of the variance at low energy $\varepsilon$ along with a vanishing Lyapunov exponent $\Gamma_1=\lim_{N\to\infty}\ln||\Pi_N||/N$, leading to the behaviour $\Gamma_2/\Gamma_1\sim\ln(1/|\varepsilon|)\to\infty$ as $\varepsilon\to0$. Our continuum description sheds new light on the Kappus-Wegner (band center) anomaly.

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

## Fractal free energy landscapes in structural glasses

### Patrick Charbonneau

^{1, 2}Jorge Kurchan^{3}Giorgio Parisi^{4, 5}Pierfrancesco Urbani^{6, 7}Francesco Zamponi^{2}*Nature Communications*, Nature Publishing Group, 2014, 5, pp.3725. <10.1038/ncomms4725>Glasses are amorphous solids whose constituent particles are caged by their neighbors and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a "roughness transition" to fractal basins. This brings about isostaticity at jamming and marginality of glassy states near jamming. Critical exponents for the basin width, the weak force distribution, and the spatial spread of quasi-contacts at jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance therefore incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control which features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here. Hitherto mysterious properties of low-temperature glasses could be explained by this approach.

- 1. Duke university [Durham]
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPS - Laboratoire de Physique Statistique de l'ENS
- 4. SMC/INFM - Department of Physics, Sapienza University of Rome
- 5. INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]
- 6. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 7. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## From generalized directed animals to the asymmetric simple exclusion process

### Nils Haug

^{1}Sergei Nechaev^{2, 3, 4}Mikhail Tamm^{4, 5}*Journal of Statistical Mechanics*, 2014, pp.P10013Using the generalized normally ordered form of words in a locally-free group of $n$ generators, we show that in the limit $n\to\infty$, the partition function of weighted directed lattice animals on a semi-infinite strip coincides with the partition function of stationary configurations of the asymmetric simple exclusion process (ASEP) with arbitrary entry/escape rates through open boundaries. We relate the features of the ASEP in the different regimes of the phase diagram to the geometric features of the associated generalized directed animals by showing the results of numerical simulations. In particular, we show how the presence of shocks at the first order transition line translates into the directed animal picture. Using the evolution equation for generalized, weighted Lukasiewicz paths, we also provide a straightforward calculation of the known ASEP generating function.

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

## From microstructural features to effective toughness in disordered brittle solids

### Vincent Démery

^{1}Laurent Ponson^{1}Alberto Rosso^{2}*Europhysics Letters*, EDP Science, 2014, 105, pp.34003The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on planar crack propagation and describe the front evolution as the propagation of a long-range elastic line within a plane with random distribution of toughness. Our study reveals two regimes: in the collective pinning regime, the macroscopic toughness can be expressed as a function of a few parameters only, namely the average and the standard deviation of the local toughness distribution and the correlation lengths of the heterogeneous toughness field; in the individual pinning regime, the passage from micro to macroscale is more subtle and the full distribution of local toughness is required to be predictive. Beyond the failure of brittle solids, our findings illustrate the complex filtering process of microscale quantities towards the larger scales into play in a broad range of systems governed by the propagation of an elastic interface in a disordered medium.

- 1. IJLRA - Institut Jean Le Rond d'Alembert
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Generalized Onsager theory for strongly anisometric patchy colloids

### H. H. Wensink

^{1}E. Trizac^{2}*Journal of Chemical Physics*, American Institute of Physics (AIP), 2014, 140, pp.024901The implications of soft 'patchy' interactions on the orientational disorder-order transition of strongly elongated colloidal rods and flat disks is studied within a simple Onsager-van der Waals density functional theory. The theory provides a generic framework for studying the liquid crystal phase behaviour of highly anisometric cylindrical colloids, which carry a distinct geometrical pattern of repulsive or attractive soft interactions localised on the particle surface. In this paper, we apply our theory to the case of charged rods and disks for which the local electrostatic interactions can be described by a screened-Coulomb potential. We consider infinitely thin rod-like cylinders with a uniform line charge and infinitely thin discotic cylinders with several distinctly different surface charge patterns. Irrespective of the backbone shape, the isotropic-nematic phase diagrams of charged colloids feature a generic destabilization of nematic order, a dramatic narrowing of the biphasic density region and a reentrant phenomenon upon reducing the electrostatic screening. At higher particle density the electrostatic repulsion leads to a complete suppression of nematic order in favour of spatially inhomogeneous liquid crystals.

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

## Geometrical origins of contractility in disordered actomyosin networks

### Lenz Martin

^{1}*Physical Review X*, 2014, 4, pp.041002Movement within eukaryotic cells largely originates from localized forces exerted by myosin motors on scaffolds of actin filaments. Although individual motors locally exert both contractile and extensile forces, large actomyosin structures at the cellular scale are overwhelmingly contractile, suggesting that the scaffold serves to favor contraction over extension. While this mechanism is well understood in highly organized striated muscle, its origin in disordered networks such as the cell cortex is unknown. Here we develop a mathematical model of the actin scaffold's local two- or three-dimensional mechanics and identify four competing contraction mechanisms. We predict that one mechanism dominates, whereby local deformations of the actin break the balance between contraction and extension. In this mechanism, contractile forces result mostly from motors plucking the filaments transversely rather than buckling them longitudinally. These findings sheds light on recent $\textit{in vitro}$ experiments, and provides a new geometrical understanding of contractility in the myriad of disordered actomyosin systems found $\textit{in vivo}$.

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

## Heat transfer between anisotropic nanopartricles: Enhancement and switching

### Roberta Incardone

^{1, 2}Thorsten Emig^{3}Matthias Krüger^{1, 2}*Europhysics Letters*, EDP Science, 2014, 106, pp.41001We theoretically study heat transfer between two anisotropic nanoparticles in vacuum, and derive closed expressions in terms of the anisotropic dipole polarizabilities. We show that transfer between two small spheroids can be many times as large as the one for two spheres of same volumes. Such increase with anisotropy is also found for the heat emission of an isolated small spheroid. Furthermore, we observe a strong dependence of transfer on the relative orientation, yielding the interpretation as a heat transfer switch. The switch quality, given as the ratio of transfer in the ''on'' and ''off'' positions, is observed to be as large as $10^3$ in the near field and even larger in the far field.

- 1. Max-Planck-Institut fur Intelligente Systeme
- 2. Institut fur Theoretische Physik IV
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Index Distribution of Cauchy Random Matrices

### Ricardo Marino

^{1}Satya N. Majumdar^{1}Grégory Schehr^{1}Pierpaolo Vivo^{1}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47, pp.055001Using a Coulomb gas technique, we compute analytically the probability $\mathcal{P}_\beta^{(C)}(N_+,N)$ that a large $N\times N$ Cauchy random matrix has $N_+$ positive eigenvalues, where $N_+$ is called the index of the ensemble. We show that this probability scales for large $N$ as $\mathcal{P}_\beta^{(C)}(N_+,N)\approx \exp\left[-\beta N^2 \psi_C(N_+/N)\right]$, where $\beta$ is the Dyson index of the ensemble. The rate function $\psi_C(\kappa)$ is computed in terms of single integrals that are easily evaluated numerically and amenable to an asymptotic analysis. We find that the rate function, around its minimum at $\kappa=1/2$, has a quadratic behavior modulated by a logarithmic singularity. As a consequence, the variance of the index scales for large $N$ as $\mathrm{Var}(N_+)\sim \sigma_C\ln N$, where $\sigma_C=2/(\beta\pi^2)$ is twice as large as the corresponding prefactor in the Gaussian and Wishart cases. The analytical results are checked by numerical simulations and against an exact finite $N$ formula which, for $\beta=2$, can be derived using orthogonal polynomials.

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

## Inferring the origin of an epidemic with a dynamic message-passing algorithm

### Andrey Y. Lokhov

^{1}Marc Mézard^{1, 2}Hiroki Ohta^{1}Lenka Zdeborová^{3}*Physical Review E*, American Physical Society, 2014, 90, pp.012801We study the problem of estimating the origin of an epidemic outbreak -- given a contact network and a snapshot of epidemic spread at a certain time, determine the infection source. Finding the source is important in different contexts of computer or social networks. We assume that the epidemic spread follows the most commonly used susceptible-infected-recovered model. We introduce an inference algorithm based on dynamic message-passing equations, and we show that it leads to significant improvement of performance compared to existing approaches. Importantly, this algorithm remains efficient in the case where one knows the state of only a fraction of nodes.

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

## Inhomogeneous and nonstationary Hall states of the CDW with quantized normal carriers

### Serguei Brazovskii

^{1}*International school-conference on electronic crystals: ECRYS-2014*, Aug 2014, Cargèse, France. 460, pp.236, Physica B: Condensed MatterWe suggest a theory for a deformable and sliding charge density wave (CDW) in the Hall bar geometry for the quantum limit when the carriers in remnant small pockets are concentrated at lowest Landau levels (LL) forming a fractionally ($\nu<1$) filled quantum Hall state. The gigantic polarizability of the CDW allows for a strong redistribution of electronic densities up to a complete charge segregation when all carriers occupy, with the maximum filling, a fraction $\nu$ of the chain length - thus forming the integer quantum Hall state, while leaving the fraction $(1-\nu)$ of the chain length unoccupied. The electric field in charged regions easily exceeds the pinning threshold of the CDW, then the depinning propagates into the nominally pinned central region via sharp domain walls. Resulting picture is that of compensated collective and normal pulsing counter-currents driven by the Hall voltage. This scenario is illustrated by numerical modeling for nonstationary distributions of the current and the electric field. This picture can interpret experiments in mesa-junctions showing depinning by the Hall voltage and the generation of voltage-controlled high frequency oscillations (Yu.I. Latyshev, P. Monceau, A.A. Sinchenko, et al, presented at ECRYS-2011, unpublished).

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

## Instanton Approach to Large $N$ Harish-Chandra-Itzykson-Zuber Integrals

### Joel Bun

^{1, 2, 3}Jean-Philippe Bouchaud^{1}Satya N. Majumdar^{2}Marc Potters^{1}*Physical Review Letters*, American Physical Society, 2014, 113, pp.070201We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.

- 1. Science et Finance
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Pole Univ Leonard de Vinci

## Interplay of anisotropy in shape and interactions in charged platelet suspensions

### Sara Jabbari-Farouji

^{1, 2}Jean-Jacques Weis^{3}Patrick Davidson^{4}Pierre Levitz^{5}Emmanuel Trizac^{2}*Journal of Chemical Physics*, American Institute of Physics (AIP), 2014, 141, pp.224510Motivated by the intriguing phase behavior of charged colloidal platelets, we investigate the structure and dynamics of charged repulsive disks by means of Monte-Carlo simulations. The electrostatic interactions are taken into account through an effective two-body potential, obtained within the non-linear Poisson-Boltzmann formalism, which has the form of anisotropic screened Coulomb potential. Recently, we showed that the original intrinsic anisotropy of the electrostatic potential in competition with excluded volume effects leads to a rich phase behavior that not only includes various liquid-crsytalline phases but also predicts the existence of novel structures composed of alternating nematic-antinematic sheets. Here, we examine the structural and dynamical signatures of each of the observed structures for both translational and rotational degrees of freedom. Finally, we discuss the influence of effective charge value and our results in relation to experimental findings on charged platelet suspensions.

- 1. LIPhy, Laboratoire Interdisciplinaire de Physique
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Laboratoire de Physique Théorique
- 4. LPS - Laboratoire de Physique des Solides
- 5. PECSA - Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques

## Islands of stability in motif distributions of random networks

### M. V. Tamm

^{1, 2}A. B. Shkarin^{3}V. A. Avetisov^{2, 4}O. V. Valba^{2, 5, 6}S. K. Nechaev^{2, 6, 7}*Physical Review Letters*, American Physical Society, 2014, 113, pp.095701We consider random non-directed networks subject to dynamics conserving vertex degrees and study analytically and numerically equilibrium three-vertex motif distributions in the presence of an external field, $h$, coupled to one of the motifs. For small $h$ the numerics is well described by the "chemical kinetics" for the concentrations of motifs based on the law of mass action. For larger $h$ a transition into some trapped motif state occurs in Erd\H{o}s-Rényi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe it in terms of a phenomenological Landau-type theory with a non-zero cubic term. A localization transition should always occur if the entropy function is non-convex. We conjecture that this phenomenon is the origin of the motifs' pattern formation in real evolutionary networks.

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

## Kovacs-like memory effect in driven granular gases

### A. Prados

^{1, 2}E. Trizac^{1}*Physical Review Letters*, American Physical Society, 2014, 112, pp.198001While memory effects have been reported for dense enough disordered systems such as glasses, we show here by a combination of analytical and simulation techniques that they are also intrinsic to the dynamics of dilute granular gases. By means of a certain driving protocol, we prepare the gas in a state where the granular temperature $T$ coincides with its long time limit. However, $T$ does not subsequently remain constant, but exhibits a non-monotonic evolution before reaching its non-equilibrium steady value. The corresponding so-called Kovacs hump displays a normal behavior for weak dissipation (as observed in molecular systems), but is reversed under strong dissipation, where it thus becomes anomalous.

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

## Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects

### Gupta Shamik

^{1}Campa Alessandro^{2}Ruffo Stefano^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2014, pp.R08001Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling, and serves as a paradigm to study synchronization. In this review, we put forward a general framework in which we discuss in a unified way known results with more recent developments obtained for a generalized Kuramoto model that includes inertial effects and noise. We describe the model from a different perspective, highlighting the long-range nature of the interaction between the oscillators, and emphasizing the equilibrium and out-of-equilibrium aspects of its dynamics from a statistical physics point of view. In the first main section, we introduce the model and discuss for the noiseless and noisy dynamics and unimodal frequency distributions the synchronization transition that occurs in the stationary state. In the second section, we introduce the generalized model, and discuss its synchronization phase diagram for unimodal frequency distributions. In the third section, we describe deviations from the mean-field setting of the Kuramoto model by considering the generalized dynamics on a one-dimensional periodic lattice on the sites of which the oscillators reside and interact with a coupling that decays as an inverse power-law of their separation. For two specific cases, namely, in the absence of noise and inertia, and in the case when the natural frequencies are the same for all the oscillators, we discuss how the long-time transition to synchrony is governed by the dynamics of the mean-field mode (zero Fourier mode) of the spatial distribution of the oscillator phases.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Department of Technology and Health
- 3. Dipartimento di Fisica e Astronomia and CSDC

## Lamplighter model of a random copolymer adsorption on a line

### L. I. Nazarov

^{1}S. K. Nechaev^{2, 3}M. V. Tamm^{4, 5}*Condensed Matter Physics*, Institute for Condensed Matter Physics, 2014, 17, pp.33002We present a model of an AB-diblock random copolymer sequential self-packaging with local quenched interactions on a one-dimensional infinite sticky substrate. It is assumed that the A-A and B-B contacts are favorable, while A-B are not. The position of a newly added monomer is selected in view of the local contact energy minimization. The model demonstrates a self-organization behavior with the nontrivial dependence of the total energy, $E$ (the number of unfavorable contacts), on the number of chain monomers, $N$: $E\sim N^{3/4}$ for quenched random equally probable distribution of A- and B-monomers along the chain. The model is treated by mapping it onto the "lamplighter" random walk and the diffusion-controlled chemical reaction of $X+X\to 0$ type with the subdiffusive motion of reagents.

- 1. Institute of Mining, Siberian Branch
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. P. N. Lebedev Physical Institute
- 4. Physics Department
- 5. Department of Applied Mathematics

## Local logarithmic correlators as limits of Coulomb gas integrals

### Raoul Santachiara

^{1}Jacopo Viti^{2}*Nuclear Physics B*, Elsevier, 2014, 882, pp.229-262We will describe how logarithmic singularities arise as limits of Coulomb Gas integrals. Our approach will combine analytic properties of the time-like Liouville structure constants, together with the recursive formula of the Virasoro conformal blocks. Although the Coulomb Gas formalism forces a diagonal coupling between the chiral and antichiral sectors of the Conformal Field Theory (CFT), we present new results for the multi-screening integrals which are potentially interesting for applications to critical statistical systems described by Logarithmic CFTs. In particular our findings extend and complement previous results, derived with Coulomb Gas methods, at $c=0$ and $c=-2$.

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

## Long-range correlations in a locally driven exclusion process

### Tridib Sadhu

^{1}Satya N. Majumdar^{2}David Mukamel^{3}*Physical Review E*, American Physical Society, 2014, 90, pp.012109We show that the presence of a driven bond in an otherwise diffusive lattice gas with simple exclusion interaction results in long-range density-density correlation in its stationary state. In dimensions $d>1$ we show that in the thermodynamic limit this correlation decays as $C(r,s)\sim (r^2+s^2)^{-d}$ at large distances $r$ and $s$ away from the drive with $|r-s|>>1$. This is derived using an electrostatic analogy whereby $C(r,s)$ is expressed as the potential due to a configuration of electrostatic charges distributed in $2d$-dimension. At bulk density $\rho=1/2$ we show that the potential is that of a localized quadrupolar charge. At other densities the same is correct in leading order in the strength of the drive and is argued numerically to be valid at higher orders.

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

## Maximal distance travelled by N vicious walkers till their survival

### Anupam Kundu

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Journal of Statistical Physics*, Springer Verlag (Germany), 2014, 157, pp.124-157We consider $N$ Brownian particles moving on a line starting from initial positions ${\bf{u}}\equiv \{u_1,u_2,\dots u_N\}$ such that $0

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

## Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at $\sqrt{s}=8$ TeV with ATLAS

### S. Franz

^{1}S. Gupta^{1}and all*Journal of High Energy Physics (JHEP)*, 2014, 09, pp.112. <10.1007/JHEP09(2014)112>Measurements of fiducial and differential cross sections are presented for Higgs boson production in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=8$ TeV. The analysis is performed in the $H \rightarrow \gamma\gamma$ decay channel using 20.3 fb$^{-1}$ of data recorded by the ATLAS experiment at the CERN Large Hadron Collider. The signal is extracted using a fit to the diphoton invariant mass spectrum assuming that the width of the resonance is much smaller than the experimental resolution. The signal yields are corrected for the effects of detector inefficiency and resolution. The $pp\rightarrow H \rightarrow \gamma\gamma$ fiducial cross section is measured to be $43.2 \pm 9.4 (stat) {}^{+3.2}_{-2.9} (syst) \pm 1.2 (lumi)$ fb for a Higgs boson of mass 125.4 GeV decaying to two isolated photons that have transverse momentum greater than 35% and 25% of the diphoton invariant mass and each with absolute pseudorapidity less than 2.37. Four additional fiducial cross sections and two cross-section limits are presented in phase space regions that test the theoretical modelling of different Higgs boson production mechanisms, or are sensitive to physics beyond the Standard Model. Differential cross sections are also presented, as a function of variables related to the diphoton kinematics and the jet activity produced in the Higgs boson events. The observed spectra are statistically limited but broadly in line with the theoretical expectations.

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

## Memory effect in uniformly heated granular gases

### E. Trizac

^{1}A. Prados^{1, 2}*Physical Review E*, American Physical Society, 2014, 90, pp.012204We evidence a Kovacs-like memory effect in a uniformly driven granular gas. A system of inelastic hard particles, in the low density limit, can reach a non-equilibrium steady state when properly forced. By following a certain protocol for the drive time dependence, we prepare the gas in a state where the granular temperature coincides with its long time value. The temperature subsequently does not remain constant, but exhibits a non-monotonic evolution with either a maximum or a minimum, depending on the dissipation, and on the protocol. We present a theoretical analysis of this memory effect, at Boltzmann-Fokker-Planck equation level, and show that when dissipation exceeds a threshold, the response can be coined anomalous. We find an excellent agreement between the analytical predictions and direct Monte Carlo simulations.

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

## Memory effects in avalanche dynamics: a key to the statistical properties of earthquakes

### E. A. Jagla

^{1}François P. Landes^{2}Alberto Rosso^{2}*Physical Review Letters*, American Physical Society, 2014, 112, pp.174301Many complex systems respond to continuous input of energy by accumulation of stress over time and sudden energy releases in the form of avalanches. Avalanches are paradigmatic non-equilibrium phenomena displaying power law size distribution and involving all the length scales in the system. Conventional avalanche models disregard memory effects and thus miss basic features observed in real systems. Notable examples are aftershocks and the anomalous exponent of the Gutenberg-Richter law which characterize earthquake statistics. We propose a model which accounts for memory effects through the introduction of viscoelastic relaxation at an intermediate time scale. We demonstrate that in the resulting dynamics, coherent oscillations of the stress field emerge spontaneously without fine tuning of any parameter. Remarkably, in two dimensions, which is relevant in seismicity, these oscillations generate instability patterns that produce realistic earthquake dynamics with the correct Gutenberg-Richter exponent.

- 1. Centro Atómico Bariloche and Instituto Balseiro
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Modeling of dislocations in a CDW junction: interference of the CDW and the normal carriers

### Alvaro Rojo Bravo

^{1}Tianyou Yi^{2}Natasha Kirova^{3, 4}Serguei Brazovskii^{1, 3}*International school-conference on electronic crystals: ECRYS-2014*, Aug 2014, Cargèse, France. 460, pp.16, Physica B: Condensed MatterWe derive and study equations for dissipative transient processes in a constraint incommensurate charge density wave (CDW) with remnant pockets or a thermal population of normal carriers. The attention was paid to give the correct conservation of condensed and normal electrons, which was problematic at presence of moving dislocation cores if working within an intuitive Ginzburg-Landau like model. We performed a numeric modelling for stationary and transient states in a rectangular geometry when the voltage V or the normal current are applied across the conducting chains. We observe creation of an array of electronic vortices, the dislocations, at or close to the junction surface; their number increases stepwise with increasing V. The dislocation core strongly concentrates the normal carriers but the CDW phase distortions almost neutralize the total charge. At other regimes, the lines of the zero CDW amplitude flash across the sample working as phase slips. The studies were inspired by, and can be applied to experiments on mesa-junctions in NbSe3 and TaS3 (Yu.I. Latyshev et al in proceedings of ECRYS 2008 and 2011).

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. South University of Science and Technology of China
- 3. International Institute of Physics
- 4. LPS - Laboratoire de Physique des Solides

## Move ordering and communities in complex networks describing the game of go

### Vivek Kandiah

^{1}Bertrand Georgeot^{1}Olivier Giraud^{2}*The European Physical Journal B*, Springer, 2014, 87, pp.246. <10.1140/epjb/e2014-50497-1>We analyze the game of go from the point of view of complex networks. We construct three different directed networks of increasing complexity, defining nodes as local patterns on plaquettes of increasing sizes, and links as actual successions of these patterns in databases of real games. We discuss the peculiarities of these networks compared to other types of networks. We explore the ranking vectors and community structure of the networks and show that this approach enables to extract groups of moves with common strategic properties. We also investigate different networks built from games with players of different levels or from different phases of the game. We discuss how the study of the community structure of these networks may help to improve the computer simulations of the game. More generally, we believe such studies may help to improve the understanding of human decision process.

- 1. LPT - Laboratoire de Physique Théorique - IRSAMC
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Multiple ordering transitions in a chiral liquid

### Pierre Ronceray

^{1, 2}Peter Harrowell^{3}*Physical Review Letters*, American Physical Society, 2014, 112, pp.017801We present here a numerical study of a lattice model of a chiral liquid. The low symmetry of the favoured local structure depresses the freezing point to reveal an exotic liquid-liquid transition characterised by the appearance of an extended chirality,prior to freezing. What mechanisms impede crystallisation in liquids with low molecular symmetry ? The ordered liquid can be readily supercooled to zero temperature, as the combination of critical slowing down and competing crystal polymorphs results in a dramatically slow crystallisation process.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. ENS Paris - École normale supérieure - Paris
- 3. Faculty of Sciences

## Near-extreme eigenvalues and the first gap of Hermitian random matrices

### Anthony Perret

^{1}Gregory Schehr^{1}*Journal of Statistical Physics*, Springer Verlag (Germany), 2014, 156, pp.843-876We study the phenomenon of "crowding" near the largest eigenvalue $\lambda_{\max}$ of random $N \times N$ matrices belonging to the Gaussian Unitary Ensemble (GUE) of random matrix theory. We focus on two distinct quantities: (i) the density of states (DOS) near $\lambda_{\max}$, $\rho_{\rm DOS}(r,N)$, which is the average density of eigenvalues located at a distance $r$ from $\lambda_{\max}$ and (ii) the probability density function of the gap between the first two largest eigenvalues, $p_{\rm GAP}(r,N)$. In the edge scaling limit where $r = {\cal O}(N^{-1/6})$, which is described by a double scaling limit of a system of unconventional orthogonal polynomials, we show that $\rho_{\rm DOS}(r,N)$ and $p_{\rm GAP}(r,N)$ are characterized by scaling functions which can be expressed in terms of the solution of a Lax pair associated to the Painlevé XXXIV equation. This provides an alternative and simpler expression for the gap distribution, which was recently studied by Witte, Bornemann and Forrester in Nonlinearity 26, 1799 (2013). Our expressions allow to obtain precise asymptotic behaviors of these scaling functions both for small and large arguments.

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

## Non-equilibrium statistical mechanics of the heat bath for two Brownian particles

### Caterina De Bacco

^{1}Fulvio Baldovin^{2}Enzo Orlandini^{2}Ken Sekimoto^{3, 4}*Physical Review Letters*, American Physical Society, 2014, 112, pp.180605We propose a new look at the heat bath for two Brownian particles, in which the heat bath as a 'system' is both perturbed and sensed by the Brownian particles. Non-local thermal fluctuation give rise to bath-mediated static forces between the particles. Based on the general sum-rule of the linear response theory, we derive an explicit relation linking these forces to the friction kernel describing the particles' dynamics. The relation is analytically confirmed in the case of two solvable models and could be experimentally challenged. Our results point out that the inclusion of the environment as a part of the whole system is important for micron- or nano-scale physics.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica e Astronomia G. Galilei and Sezione I NFN
- 3. MSC - Matière et Systèmes Complexes
- 4. LPCT - Laboratoire de Physico-Chimie Théorique

## Non-local response in a lattice gas under a shear drive

### Tridib Sadhu

^{1}Satya N. Majumdar^{2}David Mukamel^{3}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47, pp.505005In equilibrium, the effect of a spatially localised perturbation is typically confined around the perturbed region. Quite contrary to this, in a non-equilibrium stationary state often the entire system is affected. This appears to be a generic feature of non-equilibrium. We study such non-local response in the stationary state of a lattice gas with a shear drive at the boundary which keeps the system out of equilibrium. We show that a perturbation in the form of a localised blockage at the boundary, induces algebraically decaying density and current profile. In two examples, non-interacting particles and particles with simple exclusion, we analytically derive the power-law tail of the profiles.

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

## Nonequilibrium first-order transition in coupled oscillator systems with inertia and noise

### Shamik Gupta

^{1}Alessandro Campa^{2}Stefano Ruffo^{3}*Physical Review E*, American Physical Society, 2014, 89, pp.022123We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a general unimodal frequency distribution, we report here the complete phase diagram of the model in the space of dimensionless moment of inertia, temperature, and width of the frequency distribution. We demonstrate that the system undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values. We provide strong numerical evidence for the existence of both the synchronized and the incoherent phase, treating the latter analytically to obtain the corresponding linear stability threshold that bounds the first-order transition point from below. In the limit of zero noise and inertia, when the dynamics reduces to the one of the Kuramoto model, we recover the associated known continuous transition. At finite noise and inertia but in the absence of natural frequencies, the dynamics becomes that of a well-studied model of long-range interactions, the Hamiltonian mean-field model. Close to the first-order phase transition, we show that the escape time out of metastable states scales exponentially with the number of oscillators, which we explain to be stemming from the long-range nature of the interaction between the oscillators.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Complex Systems and Theoretical Physic Unit
- 3. Dipartimento di Fisica e Astronomia and CSDC

## Nonlinear waves of polarization in two-component Bose-Einstein condensates

### A. M. Kamchatnov

^{1}Y. V. Kartashov^{1}P. -É. Larré^{2}N. Pavloff^{2}*Physical Review A*, American Physical Society, 2014, 89, pp.033618Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the motion of both components is locally in phase. In the second type of waves the two components have a counter-phase local motion. In the case of different values of inter- and intra-component interaction constants, the long wave-length behavior of these two modes corresponds to two types of sound with different velocities. In the limit of weak nonlinearity and small dispersion the first mode is described by the well-known Korteweg-de Vries (KdV) equation. We show that in the same limit the second mode can be described by the Gardner (modified KdV) equation, if the intra-component interaction constants have close enough values. This leads to a rich phenomenology of nonlinear excitations (solitons, kinks, algebraic solitons, breathers) which does not exist in the KdV description.

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

## Observation of a disordered bosonic insulator from weak to strong interactions

### Chiara D Errico

^{1, 2}Eleonora Lucioni^{1, 2}Luca Tanzi^{1}Lorenzo Gori^{1}Guillaume Roux^{3}Ian P. McCulloch^{4}Thierry Giamarchi^{5}Massimo Inguscio^{1, 6}Giovanni Modugno^{1, 2}*Physical Review Letters*, American Physical Society, 2014, 113, pp.095301We employ ultracold atoms with controllable disorder and interaction to study the paradigmatic problem of disordered bosons in the full disorder-interaction plane. Combining measurements of coherence, transport and excitation spectra, we get evidence of an insulating regime extending from weak to strong interaction and surrounding a superfluid-like regime, in general agreement with the theory. For strong interaction, we reveal the presence of a strongly-correlated Bose glass coexisting with a Mott insulator.

- 1. European Laboratory for Non-linear Spectroscopy (LENS)
- 2. Istituto Nazionale di Ottica
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Centre for Engineered Quantum Systems
- 5. DPMC - Département de Physique de la Matière Condensée
- 6. INRIM

## Observation of a Strong Atom-Dimer Attraction in a Mass-Imbalanced Fermi-Fermi Mixture

### Michael Jag

^{1, 2}Matteo Zaccanti^{1, 3}Marko Cetina^{1}Rianne S. Lous^{1, 4}Florian Schreck^{1}Rudolf Grimm^{1, 4}Dmitry S. Petrov^{5}Jesper Levinsen^{6, 7}*Physical Review Letters*, American Physical Society, 2014, 112, pp.075302We investigate a mixture of ultracold fermionic $^{40}$K atoms and weakly bound $^{6}$Li$^{40}$K dimers on the repulsive side of a heteronuclear atomic Feshbach resonance. By radio-frequency spectroscopy we demonstrate that the normally repulsive atom-dimer interaction is turned into a strong attraction. The phenomenon can be understood as a three-body effect in which two heavy $^{40}$K fermions exchange the light $^{6}$Li atom, leading to attraction in odd partial-wave channels (mainly p-wave). Our observations show that mass imbalance in a fermionic system can profoundly change the character of interactions as compared to the well-established mass-balanced case.

- 1. Institut für Quantenoptik und Quanteninformation
- 2. Institut fur Experimentalphysik
- 3. CNR - Istituto Nazionale Ottica
- 4. Institut fur Experimentalphysik
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. TCM Group, Cavendish Laboratory
- 7. Aarhus Institute of Advanced Studies

## On the density of shear transformation zones in amorphous solids

### Jie Lin

^{1}Alaa Saade^{1}Edan Lerner^{1}Alberto Rosso^{2}Matthieu Wyart^{1}*Europhysics Letters*, EDP Science, 2014, 105, pp.26003We study the stability of amorphous solids, focusing on the distribution P(x) of the local stress increase x that would lead to an instability. We argue that this distribution is singular P(x)x^{\theta}, where the exponent {\theta} is non-zero if the elastic interaction between rearranging regions is non-monotonic, and increases with the interaction range. For a class of finite dimensional models we show that stability implies a lower bound on {\theta}, which is found to lie near saturation. For quadrupolar interactions these models yield {\theta} ~ 0.6 for d=2 and \theta ~ 0.4 in d=3 where d is the spatial dimension, accurately capturing previously unresolved observations in atomistic models, both in quasi-static flow and after a fast quench.

- 1. New York University, Center for Soft Matter Research
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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

### Satya N. Majumdar

^{1}Philippe Mounaix^{2}Gregory Schehr^{1}*Journal of Statistical Mechanics*, 2014, pp.P09013In the context of order statistics of discrete time random walks (RW), we investigate the statistics of the gap, $G_n$, and the number of time steps, $L_n$, between the two highest positions of a Markovian one-dimensional random walker, starting from $x_0 = 0$, after $n$ time steps (taking the $x$-axis vertical). The jumps $\eta_i = x_i - x_{i-1}$ are independent and identically distributed random variables drawn from a symmetric probability distribution function (PDF), $f(\eta)$, the Fourier transform of which has the small $k$ behavior $1 - \hat f(k) \propto |k|^\mu$, with $0 < \mu \leq 2$. For $\mu=2$, the variance of the jump distribution is finite and the RW (properly scaled) converges to a Brownian motion. For $0<\mu<2$, the RW is a L\'evy flight of index $\mu$. We show that the joint PDF of $G_n$ and $L_n$ converges to a well defined stationary bi-variate distribution $p(g,l)$ as the RW duration $n$ goes to infinity. We present a thorough analytical study of the limiting joint distribution $p(g,l)$, as well as of its associated marginals $p_{\rm gap}(g)$ and $p_{\rm time}(l)$, revealing a rich variety of behaviors depending on the tail of $f(\eta)$ (from slow decreasing algebraic tail to fast decreasing super-exponential tail). We also address the problem for a random bridge where the RW starts and ends at the origin after $n$ time steps. We show that in the large $n$ limit, the PDF of $G_n$ and $L_n$ converges to the {\it same} stationary distribution $p(g,l)$ as in the case of the free-end RW. Finally, we present a numerical check of our analytical predictions. Some of these results were announced in a recent letter [S. N. Majumdar, Ph. Mounaix, G. Schehr, Phys. Rev. Lett. {\bf 111}, 070601 (2013)].

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

## One-dimensional disordered quantum mechanics and Sinai diffusion with random absorbers

### Aurélien Grabsch

^{1}Christophe Texier^{2}Yves Tourigny^{3}*Journal of Statistical Physics*, Springer Verlag (Germany), 2014, 155, pp.237-276We study the one-dimensional Schrödinger equation with a disordered potential of the form $V (x) = \phi(x)^2+\phi'(x) + \kappa(x) $ where $\phi(x)$ is a Gaussian white noise with mean $\mu g$ and variance $g$, and $\kappa(x)$ is a random superposition of delta functions distributed uniformly on the real line with mean density $\rho$ and mean strength $v$. Our study is motivated by the close connection between this problem and classical diffusion in a random environment (the Sinai problem) in the presence of random absorbers~: $\phi(x)$ models the force field acting on the diffusing particle and $\kappa(x)$ models the absorption properties of the medium in which the diffusion takes place. The focus is on the calculation of the complex Lyapunov exponent $ \Omega(E) = \gamma(E) - \mathrm{i} \pi N(E) $, where $N$ is the integrated density of states per unit length and $\gamma$ the reciprocal of the localisation length. By using the continuous version of the Dyson-Schmidt method, we find an exact formula, in terms of a Hankel function, in the particular case where the strength of the delta functions is exponentially-distributed with mean $v=2g$. Building on this result, we then solve the general case -- in the low-energy limit -- in terms of an infinite sum of Hankel functions. Our main result, valid without restrictions on the parameters of the model, is that the integrated density of states exhibits the power law behaviour $$ N(E) \underset{E\to0+}{\sim} E^\nu \hspace{0.5cm} \mbox{where } \nu=\sqrt{\mu^2+2\rho/g}\:. $$ This confirms and extends several results obtained previously by approximate methods.

- 1. ENS Cachan - École normale supérieure - Cachan
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. School of Mathematics [Bristol]

## Outage Capacity for the Optical MIMO Channel

### Apostolos Karadimitrakis

^{1}Aris L. Moustakas^{1, 2}Pierpaolo Vivo^{3}#### France. 60, pp.4370, 2014, Information theory IEEE Transactions on

MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. In this paper we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant cross talk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in the transmission may be parameterized by a number of unutilized channels in the fiber. We analyze the system in a dual fashion. First, we evaluate a closed-form expression for the outage probability, which is handy for small matrices. We also apply the asymptotic approach, in particular the Coulomb gas method from statistical mechanics, to obtain closed-form results for the ergodic mutual information, its variance as well as the outage probability for Gaussian input in the limit of large number of cores/modes. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.

- 1. UNIV. ATHENS - University of Athens, Greece
- 2. E3S - Supélec Sciences des Systèmes - EA4454
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Phase transitions and edge scaling of number variance in Gaussian random matrices

### Ricardo Marino

^{1}Satya N. Majumdar^{1}Grégory Schehr^{1}Pierpaolo Vivo^{1}*Physical Review Letters*, American Physical Society, 2014, 112, pp.254101We consider $N\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\sqrt{2},\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the probability $\mathcal{P}_{\scriptscriptstyle N,L}(N_L)$ that $N_L$ eigenvalues lie within the box $[-L,L]$. This probability scales as $\mathcal{P}_{\scriptscriptstyle N,L}(N_L=\kappa_L N)\approx\exp\left(-{\beta} N^2 \psi_L(\kappa_L)\right)$, where $\beta$ is the Dyson index of the ensemble and $\psi_L(\kappa_L)$ is a $\beta$-independent rate function that we compute exactly. We identify three regimes as $L$ is varied: (i) $\, N^{-1}\ll L<\sqrt{2}$ (bulk), (ii) $\ L\sim\sqrt{2}$ on a scale of $\mathcal{O}(N^{-{2}/{3}})$ (edge) and (iii) $\ L > \sqrt{2}$ (tail). We find a dramatic non-monotonic behavior of the number variance $V_N(L)$ as a function of $L$: after a logarithmic growth $\propto \ln (N L)$ in the bulk (when $L \sim {\cal O}(1/N)$), $V_N(L)$ decreases abruptly as $L$ approaches the edge of the semi-circle before it decays as a stretched exponential for $L > \sqrt{2}$. This "drop-off" of $V_N(L)$ at the edge is described by a scaling function $\tilde V_{\beta}$ which smoothly interpolates between the bulk (i) and the tail (iii). For $\beta = 2$ we compute $\tilde V_2$ explicitly in terms of the Airy kernel. These analytical results, verified by numerical simulations, directly provide for $\beta=2$ the full statistics of particle-number fluctuations at zero temperature of 1d spinless fermions in a harmonic trap.

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

## Phase transitions in the condition number distribution of Gaussian random matrices

### Isaac Pérez Castillo

^{1}Eytan Katzav^{2}Pierpaolo Vivo^{3, 4}*Physical Review E*, American Physical Society, 2014, 90, pp.050103We study the statistics of the condition number $\kappa=\lambda_{\mathrm{max}}/\lambda_{\mathrm{min}}$ (the ratio between largest and smallest squared singular values) of $N\times M$ Gaussian random matrices. Using a Coulomb fluid technique, we derive analytically and for large $N$ the cumulative $\mathcal{P}[\kappa

- 1. Departamento de Sistemas Complejos, Instituto de Física, UNAM
- 2. Racah Institute of Physics - Racah Institute of Physics
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Department of Mathematics, King's College London

## Polydispersity and optimal relaxation in the hard sphere fluid

### Matthieu Barbier

^{1}Emmanuel Trizac^{1}*Journal of Statistical Physics*, Springer Verlag (Germany), 2014, 154, pp.1365-1390We consider the mass heterogeneity in a gas of polydisperse hard particles as a key to optimizing a dynamical property: the kinetic relaxation rate. Using the framework of the Boltzmann equation, we study the long time approach of a perturbed velocity distribution toward the equilibrium Maxwellian solution. We work out the cases of discrete as well as continuous distributions of masses, as found in dilute fluids of mesoscopic particles such as granular matter and colloids. On the basis of analytical and numerical evidence, we formulate a dynamical equipartition principle that leads to the result that no such continuous dispersion in fact minimizes the relaxation time, as the global optimum is characterized by a finite number of species. This optimal mixture is found to depend on the dimension d of space, ranging from five species for d=1 to a single one for d>=4. The role of the collisional kernel is also discussed, and extensions to dissipative systems are shown to be possible.

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

## Quantum Flutter: Signatures and Robustness

### Michael Knap

^{1, 2, 3}Charles J. M. Mathy^{3, 4}Martin Ganahl^{2}Mikhail B. Zvonarev^{5}Eugene Demler^{4}*Physical Review Letters*, American Physical Society, 2014, 112, pp.015302We investigate the motion of an impurity particle injected with finite velocity into an interacting one-dimensional quantum gas. Using large-scale numerical simulations based on matrix product states, we observe and quantitatively analyze long-lived oscillations of the impurity momentum around a non-zero saturation value, called quantum flutter. We show that the quantum flutter frequency is equal to the energy difference between two branches of collective excitations of the model. We propose an explanation of the finite saturation momentum of the impurity based on the properties of the edge of the excitation spectrum. Our results indicate that quantum flutter exists away from integrability, and provide parameter regions in which it could be observed in experiments with ultracold atoms using currently available technology.

- 1. Department of Physics
- 2. Institute of Theoretical and Computational Physics
- 3. CFA - Harvard-Smithsonian Center for Astrophysics
- 4. Department of Physics
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Quasiparticle spectroscopy as a probe of the topological phase in graphene with heavy adatoms

### Paul Soulé

^{1, 2}Marcel Franz^{2, 3}#### 4 pages, 2 figures; Version 2 : references added, minor changes. 2014

Electrons in graphene with heavy adatoms (such as In or Tl) have been predicted to form a 2D topological insulator phase with a substantial spectral gap potentially suitable for future practical applications. In order to facilitate the ongoing experimental efforts to identify this phase we perform a theoretical study of its spectral properties in a model graphene system with randomly distributed adatoms. Our extensive modeling shows that random heavy adatoms produce a full spectral gap (as opposed to a mobility gap) accompanied by distinctive quasiparticle interference patterns observable by means of Fourier-transform scanning tunneling spectroscopy.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Department of Physics and Astronomy
- 3. Quantum Matter Institute

## Relevance of electron spin dissipative processes on Dynamic Nuclear Polarization via Thermal Mixing

### Sonia Colombo Serra

^{1}Marta Filibian^{2}Pietro Carretta^{3}Alberto Rosso^{4}Fabio Tedoldi^{1}*Physical Chemestry Chemical Physics*, 2014, 16, pp.753-764The available theoretical approaches aiming at describing Dynamic Nuclear spin Polarization (DNP) in solutions containing molecules of biomedical interest and paramagnetic centers are not able to model the behaviour observed upon varying the concentration of trityl radicals or the polarization enhancement caused by moderate addition of gadolinium complexes. In this manuscript, we first show experimentally that the nuclear steady state polarization reached in solutions of pyruvic acid with 15 mM trityl radicals is substantially independent from the average internuclear distance. This evidences a leading role of electron (over nuclear) spin relaxation processes in determining the ultimate performances of DNP. Accordingly, we have devised a variant of the Thermal Mixing model for inhomogenously broadened electron resonance lines which includes a relaxation term describing the exchange of magnetic anisotropy energy of the electron spin system with the lattice. Thanks to this additional term, the dependence of the nuclear polarization on the electron concentration can be properly accounted for. Moreover, the model predicts a strong increase of the final polarization on shortening the electron spin-lattice relaxation time, providing a possible explanation for the effect of gadolinium doping.

- 1. Centro Ricerche Bracco
- 2. CNISM - Dipartimento di Fisica and Unità
- 3. CNISM - Dipartimento di Fisica and Unità
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Reweighted belief propagation and quiet planting for random K-SAT

### Florent Krzakala

^{1}Marc Mézard^{2, 3}Lenka Zdeborová^{4}*Journal on Satisfiability, Boolean Modeling and Computation*, IOS Press, 2014, 8, pp.149We study the random K-satisfiability problem using a partition function where each solution is reweighted according to the number of variables that satisfy every clause. We apply belief propagation and the related cavity method to the reweighted partition function. This allows us to obtain several new results on the properties of random K-satisfiability problem. In particular the reweighting allows to introduce a planted ensemble that generates instances that are, in some region of parameters, equivalent to random instances. We are hence able to generate at the same time a typical random SAT instance and one of its solutions. We study the relation between clustering and belief propagation fixed points and we give a direct evidence for the existence of purely entropic (rather than energetic) barriers between clusters in some region of parameters in the random K-satisfiability problem. We exhibit, in some large planted instances, solutions with a non-trivial whitening core; such solutions were known to exist but were so far never found on very large instances. Finally, we discuss algorithmic hardness of such planted instances and we determine a region of parameters in which planting leads to satisfiable benchmarks that, up to our knowledge, are the hardest known.

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

## Scaling description of the yielding transition in soft amorphous solids at zero temperature

### Jie Lin

^{1, 2}Edan Lerner^{3}Alberto Rosso^{4}Matthieu Wyart^{3}*Proceedings of the National Academy of Sciences U S A*, National Academy of Sciences, 2014, 111, pp.14382Yield stress materials flow if a sufficiently large shear stress is ap- plied. Although such materials are ubiquitous and relevant for indus- try, there is no accepted microscopic description of how they yield, even in the simplest situations where temperature is negligible and where flow inhomogeneities such as shear bands or fractures are ab- sent. Here we propose a scaling description of the yielding transition in amorphous solids made of soft particles at zero temperature. Our description makes a connection between the Herschel-Bulkley expo- nent characterizing the singularity of the flow curve near the yield stress {\Sigma}c, the extension and duration of the avalanches of plasticity observed at threshold, and the density P(x) of soft spots, or shear transformation zones, as a function of the stress increment x be- yond which they yield. We argue that the critical exponents of the yielding transition can be expressed in terms of three independent exponents {\theta}, df and z, characterizing respectively the density of soft spots, the fractal dimension of the avalanches, and their duration. Our description shares some similarity with the depinning transition that occurs when an elastic manifold is driven through a random potential, but also presents some striking differences. We test our arguments in an elasto-plastic model, an automaton model similar to those used in depinning, but with a different interaction kernel, and find satisfying agreement with our predictions both in two and three dimensions.

- 1. Division of Parasitology
- 2. Parasitology, Center of Infectious Diseases
- 3. New York University, Center for Soft Matter Research
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Scaling properties of field-induced superdiffusion in Continous Time Random Walks

### R. Burioni

^{1, 2}G. Gradenigo^{3, 4}A. Sarracino^{3}A. Vezzani^{5, 6}A. Vulpiani^{7}*Small system nonequilibrium fluctuations, dynamics and stochastics, and anomalous behavior*, China. 62, pp.514, 2014, Communications in Theoretical PhysicsWe consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.

- 1. Fisica
- 2. INFN
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. CEA - CEA Saclay
- 5. Fisica
- 6. Fisica
- 7. INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]

## Shortest node-disjoint paths on random graphs

### Caterina De Bacco

^{1}Silvio Franz^{1}David Saad^{2}Chi Ho Yeung^{2, 3, 4}*Journal of Statistical Mechanics*, 2014, pp.P07009A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process global information and distribute paths optimally. Statistical properties such as scaling with system size and number of paths, average path-length and the transition to the frustrated regime are analysed. The performance of the suggested algorithm is evaluated through a comparison against a greedy algorithm.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Aston University
- 3. Department of Physics
- 4. Department of Science and Environmental Studies

## SO(5) symmetry in the quantum Hall effect in graphene

### Fengcheng Wu

^{1}Inti Sodemann^{1}Yasufumi Araki^{1}Allan H. MacDonald^{1}Thierry Jolicoeur^{2}*Physical Review B (Condensed Matter)*, American Physical Society, 2014, pp.235432Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect in graphene is dominated by long-range Coulomb interactions which are invariant under rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at most filling factors, and also weakly broken by atomic scale valley-dependent and valley-exchange interactions with coupling constants $g_{z}$ and $g_{\perp}$. In this paper we demonstrate that when $g_{z}=-g_{\perp}$ an exact SO(5) symmetry survives which unifies the N\'eel spin order parameter of the antiferromagnetic state and the $XY$ valley order parameter of the Kekul\'e distortion state into a single five-component order parameter. The proximity of the highly insulating quantum Hall state observed in graphene at $\nu=0$ to an ideal SO(5) symmetric quantum Hall state remains an open experimental question. We illustrate the physics associated with this SO(5) symmetry by studying the multiplet structure and collective dynamics of filling factor $\nu=0$ quantum Hall states based on exact-diagonalization and low-energy effective theory approaches. This allows to illustrate how manifestations of the SO(5) symmetry would survive even when it is weakly broken.

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

## Spectral density of the quantum Ising model in two fields: Gaussian and multi-Gaussian approximations

### Y. Y. Atas

^{1}E. Bogomolny^{1}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47, pp.335201Spectral density of quantum Ising model in two fields for large but finite number of spins $N$, is discussed in detail. When all coupling constants are of the same order, spectral densities in the bulk are well approximated by a Gaussian function which is typical behaviour for many-body models with short-range interactions. The main part of the paper is devoted to the investigation of a different characteristic case when spectral densities have peaks related with strong degeneracies of unperturbed states in certain limits of coupling constants. In the strict limit $N\to\infty$, peaks overlap and disappear but for values of $N$ accessible in numerical calculations they often strongly influence spectral densities and other quantities as well. A simple method is developed which permits to find general approximation formulae for multi-peak structure of spectral density in good agreement with numerics.

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

## Spinon excitation spectra of the $J_1$-$J_2$ chain from analytical calculations in the dimer basis and exact diagonalization

### Lavarélo Arthur

^{1}Roux Guillaume^{1}*The European Physical Journal B*, Springer, 2014, 87, pp.229The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation at $J_2=9/17J_1$ [as in S. Brehmer \emph{et al.}, J. Phys.: Condens. Matter \textbf{10}, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.

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

## Statistics of the first passage time of Brownian motion conditioned by maximum value or area

### Michael J. Kearney

^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47, pp.465001We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated.

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

## Strong pinning of propagation fronts in adverse flow

### Thomas Gueudré

^{1}Awadhesh Kumar Dubey^{2}Laurent Talon^{2}Alberto Rosso^{3}*Physical Review E*, American Physical Society, 2014, 89, pp.041004Reaction fronts evolving in a porous medium exhibit a rich dynamical behaviour. In presence of an adverse flow, experiments show that the front slows down and eventually gets pinned, displaying a particular sawtooth shape. Extensive numerical simulations of the hydrodynamic equations confirm the experimental observations. Here we propose a stylized model, predicting two possible outcomes of the experiments for large adverse flow: either the front develops a sawtooth shape, or it acquires a complicated structure with islands and overhangs. A simple criterion allows to distinguish between the two scenarios and its validity is reproduced by direct hydrodynamical simulations. Our model gives a better understanding of the transition and is relevant in a variety of domains, when the pinning regime is strong and only relies on a small number of sites.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. FAST - Fluides, automatique, systèmes thermiques
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Synchronization transitions in globally coupled rotors in presence of noise and inertia: Exact results

### Maxim Komarov

^{1, 2}Shamik Gupta^{3}Arkady Pikovsky^{1, 2}*Europhysics Letters*, EDP Science, 2014, 106, pp.40003We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes previously studied Sakaguchi-Kuramoto, Hamiltonian and Brownian mean-field, and Tanaka-Lichtenberg-Oishi and Acebrón-Bonilla-Spigler models. We derive an exact solution of the self-consistent equations for the order parameter in the stationary state, valid for arbitrary parameters in the dynamics, and demonstrate nontrivial phase transitions to synchrony that include reentrant synchronous regimes.

- 1. UNIPOTSDAM - Department of Physics and Astronomie, Univ. Potsdam
- 2. Department of Control Theory
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Taking one charge off a two-dimensional Wigner crystal

### Moritz Antlanger

^{1, 2}Martial Mazars^{1}Ladislav Šamaj^{3, 4}Gerhard Kahl^{2}Emmanuel Trizac^{4}#### LPT-ORSAY 14-10. 17 pages, 11 figures. 2014

A planar array of identical charges at vanishing temperature forms a Wigner crystal with hexagonal symmetry. We take off one (reference) charge in a perpendicular direction, hold it fixed, and search for the ground state of the whole system. The planar projection of the reference charge should then evolve from a six-fold coordination (center of a hexagon) for small distances to a three-fold arrangement (center of a triangle), at large distances $d$ from the plane. The aim of this paper is to describe the corresponding non-trivial lattice transformation. For that purpose, two numerical methods (direct energy minimization and Monte Carlo simulations), together with an analytical treatment, are presented. Our results indicate that the $d=0$ and $d\to\infty$ limiting cases extend for finite values of $d$ from the respective starting points into two sequences of stable states, with intersecting energies at some value $d_t$; beyond this value the branches continue as metastable states.

- 1. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 2. Institut für Theoretische Physik and Center for Computational Materials Science
- 3. Institute of Physics
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The effect of disorder geometry on the critical force in disordered elastic systems

### V. Démery

^{1}V. Lecomte^{2}A. Rosso^{3}*Journal of Statistical Mechanics : Theory and Experiment*, 2014, P03009, 20 p. <10.1088/1742-5468/2014/03/P03009>- 1. IJLRA - Institut Jean Le Rond d'Alembert
- 2. LPMA - Laboratoire de Probabilités et Modèles Aléatoires
- 3. Laboratoire Physique Théorique et Modèles Statistiques (UMR CNRS 8626), Université de Paris-Sud, Orsay Cedex,

## The role of the glassy dynamics and thermal mixing in the dynamic nuclear polarization and relaxation mechanisms of pyruvic acid

### Marta Filibian

^{1}Sonia Colombo Serra^{2}Marco Moscardini^{1}Alberto Rosso^{3}Fabio Tedoldi^{2}Pietro Carretta^{1}*Physical Chemistry Chemical Physics*, Royal Society of Chemistry, 2014, 16, pp.27025The temperature dependence of $^1$H and $^{13}$C nuclear spin-lattice relaxation rate $1/T_1$ has been studied between 4.2 K and 1.6 K in pure pyruvic acid and in pyruvic acid containing trityl radicals at a concentration of 15 mM. The temperature dependence of $1/T_1$ is found to follow a quadratic power law for both nuclei in the two samples. Remarkably that is the same temperature dependence found also for the electron spin-lattice relaxation rate in the sample containing radicals. Dynamical nuclear polarization experiments on this latter sample show that below 4 K $^{13}$C build up rate and $1/T_1$ scale with $1/T_{1e}$ and their values are quantitatively consistent with the presence of a thermal mixing regime between the nuclear and electron spin reservoirs. These results are explained by considering the effect of the pyruvic acid glassy dynamics on the relaxation rates and by assuming that below 4 K dynamical nuclear polarization is driven by a very good thermal contact between the nuclear and electron spin reservoirs.

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

## The three-body parameter for Efimov states in lithium-6

### Huang Bo

^{1}O'Hara Kenneth M.^{2, 3}Grimm Rudolf^{1, 3}Hutson Jeremy M.^{4}Petrov Dmitry S.^{5}*Physical Review A*, American Physical Society, 2014, 90, pp.043636We present a state-of-the-art reanalysis of experimental results on Efimov resonances in the three-fermion system of $^6$Li. We discuss different definitions of the 3-body parameter (3BP) for Efimov states, and adopt a definition that excludes effects due to deviations from universal scaling for low-lying states. We develop a finite-temperature model for the case of three distinguishable fermions and apply it to the excited-state Efimov resonance to obtain the most accurate determination to date of the 3BP in an atomic three-body system. Our analysis of ground-state Efimov resonances in the same system yields values for the three-body parameter that are consistent with the excited-state result. Recent work has suggested that the reduced 3BP for atomic systems is a near-universal quantity, almost independent of the particular atom involved. However, the value of the 3BP obtained for $^6$Li is significantly ($\sim 20$%) different from that previously obtained from the excited-state resonance in Cs. The difference between these values poses a challenge for theory.

- 1. Institut für Experimentalphysik
- 2. Pennsylvania State University
- 3. ICOQI - Institut für Quantenoptik und Quanteninformation
- 4. JQC - Joint Quantum Centre
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The two scenarios for quantum multifractality breakdown

### Rémy Dubertrand

^{1}Ignacio García-Mata^{2}Bertrand Georgeot^{1}Olivier Giraud^{3}Gabriel Lemarié^{1}J. Martin^{4}*Physical Review Letters*, American Physical Society, 2014, 112, pp.234101. <10.1103/PhysRevLett.112.234101>We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Our results suggest that quantum multifractality breakdown is universal and follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications.

- 1. Information et Chaos Quantiques (LPT)
- 2. Instituto de Investigaciones Físicas de Mar del Plata
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Institut de Physique Nucléaire, Atomique et de Spectroscopie

## Thinking outside the box: fluctuations and finite size effects

### Dario Villamaina

^{1}Emmanuel Trizac^{1}*European Journal of Physics*, Institute of Physics: Hybrid Open Access, 2014, 35, pp.3The isothermal compressibility of an interacting or non interacting system may be extracted from the fluctuations of the number of particles in a well chosen control volume. Finite size effects are prevalent and should then be accounted for to obtain a meaningful, thermodynamic compressibility. In the traditional computational setup where a given simulation box is replicated with periodic boundary conditions, we study particle number fluctuations outside the box (i.e. when the control volume exceeds the box itself), which bear relevant thermodynamic information. We also investigate the related problem of extracting the compressibility from the structure factor in the small wave-vector limit ($k\to 0$). The calculation should be restricted to the discrete set of wave-vectors $k$ that are compatible with the periodicity of the system, and we assess the consequences of considering other $k$ values, a widespread error among beginners.

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

## Thomas precession, persistent spin currents and quantum forces

### Stephane Ouvry

^{1}Leonid Pastur^{2}Andrey Yanovsky^{2}*Europhysics Letters*, EDP Science, 2014, 106, pp.18001We consider T-invariant spin currents induced by spin-orbit interactions which originate from the confined motion of spin carriers in nanostructures. The resulting Thomas spin precession is a fundamental and purely kinematic relativistic effect occurring when the acceleration of carriers is not parallel to their velocity. In the case, where the carriers (e.g. electrons) have magnetic moment the forces due to the electric field of the spin current can, in certain conditions, exceed the van der Waals-Casimir forces by several orders of magnitude. We also discuss a possible experimental set-up tailored to use these forces for checking the existence of a nonzero anomalous magnetic moment of the photon.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Low Temperature Physics Institute, Kharkiv

## Three-Body Interacting Bosons in Free Space

### D. S. Petrov

^{1}*Physical Review Letters*, American Physical Society, 2014, 112, pp.103201We propose a method of controlling two- and three-body interactions in an ultracold Bose gas in any dimension. The method requires us to have two coupled internal single-particle states split in energy such that the upper state is occupied virtually but amply during collisions. By varying system parameters one can switch off the two-body interaction while maintaining a strong three-body one. The mechanism can be implemented for dipolar bosons in the bilayer configuration with tunnelling or in an atomic system by using radio-frequency fields to couple two hyperfine states. One can then aim to observe a purely three-body-interacting gas, dilute self-trapped droplets, the paired superfluid phase, Pfaffian state, and other exotic phenomena.

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

## Top eigenvalue of a random matrix: large deviations and third order phase transition

### Satya N. Majumdar

^{1}Gregory Schehr^{1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2014, pp.P01012We study the fluctuations of the largest eigenvalue $\lambda_{\max}$ of $N \times N$ random matrices in the limit of large $N$. The main focus is on Gaussian $\beta$-ensembles, including in particular the Gaussian orthogonal ($\beta=1$), unitary ($\beta=2$) and symplectic ($\beta = 4$) ensembles. The probability density function (PDF) of $\lambda_{\max}$ consists, for large $N$, of a central part described by Tracy-Widom distributions flanked, on both sides, by two large deviations tails. While the central part characterizes the typical fluctuations of $\lambda_{\max}$ -- of order ${\cal O}(N^{-2/3})$ --, the large deviations tails are instead associated to extremely rare fluctuations -- of order ${\cal O}(1)$. Here we review some recent developments in the theory of these extremely rare events using a Coulomb gas approach. We discuss in particular the third-order phase transition which separates the left tail from the right tail, a transition akin to the so-called Gross-Witten-Wadia phase transition found in 2-d lattice quantum chromodynamics. We also discuss the occurrence of similar third-order transitions in various physical problems, including non-intersecting Brownian motions, conductance fluctuations in mesoscopic physics and entanglement in a bipartite system.

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

## Topological transition in disordered planar matching: combinatorial arcs expansion

### Andrey Y. Lokhov

^{1}Olga V. Valba^{2, 3}Sergei K. Nechaev^{1, 4, 3}Mikhail V. Tamm^{5, 3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2014, pp.P12004In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yielding complete planar matching solutions only above a critical density threshold. We develop a combinatorial procedure of arcs expansion that explicitly takes into account the contribution of short arcs, and allows to obtain an accurate analytical estimation of the critical value by reducing the global constrained problem to a set of local ones. As an application to a toy representation of the RNA secondary structures, we suggest generalized models that incorporate a one-to-one correspondence between the contact matrix and the RNA-type sequence, thus giving sense to the notion of effective non-integer alphabets.

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

## Ultrafast switching to a stable hidden topologically protected quantum state in an electronic crystal

### L. Stojchevska

^{1, 2}I. Vaskivskyi^{1}T. Mertelj^{1}P. Kusar^{1}D. Svetin^{1}S. Brazovskii^{3, 4}D. Mihailovic^{1, 2, 5}*Science*, American Association for the Advancement of Science, 2014, 344, pp.177-180Hidden states of matter with novel and unusual properties may be created if a system out of equilibrium can be induced to follow a trajectory to a state which is inaccessible or does not even exist under normal equilibrium conditions. Here we report on the discovery of a hidden (H) topologically protected electronic state in a layered dichalcogenide 1T-TaS2 crystal reached as a result of a quench caused by a single 35 fs laser pulse. The properties of the H state are markedly different from any other state of the system: it exhibits a large drop of electrical resistance, strongly modified single particle and collective mode spectra and a marked change of optical reflectivity. Particularly important and unusual, the H state is stable for an arbitrarily long time until a laser pulse, electrical current or thermal erase procedure is applied, causing it to revert to the thermodynamic ground state. Major observed events can be reproduced by a kinetic model describing the conversion of photo excited electrons and holes into an electronically ordered crystal, thus converting a Mott insulator to a conducting H state. Its long-time stability follows from the topological protection of the number of periods in the electronic crystal.

- 1. Department of Complex Matter
- 2. Jozef Stefan International Postgraduate School
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. International Institute of Physics
- 5. CENN Nanocenter

## Universal covariance formula for linear statistics on random matrices

### Fabio Deelan Cunden

^{1, 2}Pierpaolo Vivo^{3}*Physical Review Letters*, American Physical Society, 2014, 113, pp.070202We derive an analytical formula for the covariance $\mathrm{Cov}(A,B)$ of two smooth linear statistics $A=\sum_i a(\lambda_i)$ and $B=\sum_i b(\lambda_i)$ to leading order for $N\to\infty$, where $\{\lambda_i\}$ are the $N$ real eigenvalues of a general one-cut random-matrix model with Dyson index $\beta$. The formula, carrying the universal $1/\beta$ prefactor, depends on the random-matrix ensemble only through the edge points $[\lambda_-,\lambda_+]$ of the limiting spectral density. For $A=B$, we recover in some special cases the classical variance formulas by Beenakker and Dyson-Mehta, clarifying the respective ranges of applicability. Some choices of $a(x)$ and $b(x)$ lead to a striking \emph{decorrelation} of the corresponding linear statistics. We provide two applications - the joint statistics of conductance and shot noise in ideal chaotic cavities, and some new fluctuation relations for traces of powers of random matrices.

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

## Universal Order and Gap Statistics of Critical Branching Brownian Motion

### Kabir Ramola

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Physical Review Letters*, American Physical Society, 2014, 112, pp.210602We study the order statistics of one dimensional branching Brownian motion in which particles either diffuse (with diffusion constant $D$), die (with rate $d$) or split into two particles (with rate $b$). At the critical point $b=d$ which we focus on, we show that, at large time $t$, the particles are collectively bunched together. We find indeed that there are two length scales in the system: (i) the diffusive length scale $\sim \sqrt{Dt}$ which controls the collective fluctuations of the whole bunch and (ii) the length scale of the gap between the bunched particles $\sim \sqrt{D/b}$. We compute the probability distribution function $P(g_k,t|n)$ of the $k$th gap $g_k = x_k - x_{k+1}$ between the $k$th and $(k+1)$th particles given that the system contains exactly $n>k$ particles at time $t$. We show that at large $t$, it converges to a stationary distribution $P(g_k,t\to \infty|n) = p(g_k|n)$ with an algebraic tail $p(g_k|n) \sim 8(D/b) g_k^{-3}$, for $g_k \gg 1$, independent of $k$ and $n$. We verify our predictions with Monte Carlo simulations.

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

## Universal properties of branching random walks in confined geometries

### Clélia De Mulatier

^{1, 2}Alain Mazzolo^{2}Andrea Zoia^{2}*Europhysics Letters*, EDP Science, 2014, 107, pp.30001Characterizing the occupation statistics of a radiation flow through confined geometries is key to such technological issues as nuclear reactor design and medical diagnosis. This amounts to assessing the distribution of the travelled length $\ell$ and the number of collisions $n$ performed by the underlying stochastic transport process, for which remarkably simple Cauchy-like formulas were established in the case of branching Pearson random walks with exponentially distributed jumps. In this Letter, we show that such formulas strikingly carry over to the much broader class of branching processes with arbitrary jumps, provided that scattering is isotropic and the average jump size is finite.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. DM2S - Département de Modélisation des Systèmes et Structures

## Universal statistics of longest lasting records of random walks and Lévy flights

### Claude Godreche

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}#### t14/073. 23 pages, 4 figures, Typos corrected. 2014

We study the record statistics of random walks after $n$ steps, $x_0, x_1,\ldots, x_n$, with arbitrary symmetric and continuous distribution $p(\eta)$ of the jumps $\eta_i = x_i - x_{i-1}$. We consider the age of the records, i.e. the time up to which a record survives. Depending on how the age of the current last record is defined, we propose three distinct sequences of ages (indexed by $\alpha$ = I, II, III) associated to a given sequence of records. We then focus on the longest lasting record, which is the longest element among this sequence of ages. To characterize the statistics of these longest lasting records, we compute: (i) the probability that the record of the longest age is broken at step $n$, denoted by $Q^{\alpha}(n)$, which we call the probability of record breaking and: (ii) the duration of the longest lasting record, $\ell_{\max}^{\alpha}(n)$. We show that both $Q^{\alpha}(n)$ and the full statistics of $\ell_{\max}^{\alpha}(n)$ are universal, i.e. independent of the jump distribution $p(\eta)$. We compute exactly the large $n$ asymptotic behaviors of $Q^{\alpha}(n)$ as well as $\langle \ell_{\max}^{\alpha}(n)\rangle$ (when it exists) and show that each case gives rise to a different universal constant associated to random walks (including Lévy flights). While two of them appeared before in the excursion theory of Brownian motion, for which we provide here a simpler derivation, the third case gives rise to a non-trivial new constant $C^{\rm III} = 0.241749 \ldots$ associated to the records of random walks. Other observables characterizing the ages of the records, exhibiting an interesting universal behavior, are also discussed.

- 1. Institut de Physique Théorique CEA Saclay
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Velocity filtration and temperature inversion in a system with long-range interactions

### Lapo Casetti

^{1, 2}Shamik Gupta^{3}#### 6 pages, 9 figures, epj macros. 2014

Temperature inversion due to velocity filtration, a mechanism originally proposed to explain the heating of the solar corona, is demonstrated to occur also in a simple paradigmatic model with long-range interactions, the Hamiltonian mean-field model. Using molecular dynamics simulations, we show that when the system settles into an inhomogeneous quasi-stationary state in which the velocity distribution has suprathermal tails, the temperature and density profiles are anticorrelated: denser parts of the system are colder than dilute ones. We argue that this may be a generic property of long-range interacting systems.

- 1. INAF-Osservatorio Astrofisico di Arcetri
- 2. Dipartimento di Fisica e Astronomia and CSDC
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Waiting time distribution for trains of quantized electron pulses

### Mathias Albert

^{1}*PHYS. REV. B*, 2014, 90, pp.10We consider a sequence of quantized Lorentzian pulses of noninteracting electrons impinging on a quantum point contact and study the waiting time distribution (WTD), for any transmission and any number of pulses. As the degree of overlap between the electronic wave functions is tuned, the WTD reveals how the correlations between particles are modified. In the weak overlap regime, the WTD is made of several equidistant peaks, separated by the same period as the incoming pulses, contained in an almost exponentially decaying envelope. In the other limit, the WTD of a single quantum channel subjected to a constant voltage is recovered. In both cases, the WTD stresses the difference between the fluctuations induced by the scatterer and the ones encoded in the incoming quantum state. A clear crossover between these two situations is studied with numerical and analytical calculations based on scattering theory.

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

## Winding statistics of a Brownian particle on a ring

### Anupam Kundu

^{1}Alain Comtet^{1, 2}Satya N. Majumdar^{1}*Journal of Physics A: Mathematical and Theoretical*, Institute of Physics: Hybrid Open Access, 2014, 47 (38), pp.385001We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes till time t. Using a method based on the renewal properties of Brownian walker, we find exact analytical expressions of these distributions. This method serves as an alternative to the standard path integral techniques which are not always easily adaptable for certain observables. For large t, we show that these distributions have Gaussian scaling forms. We also compute large deviation functions associated to these distributions characterizing atypically large fluctuations. We provide numerical simulations in support of our analytical results.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IHP - Institut Henri Poincaré