# Publications 2012

• ## A two-dimensional one component plasma and a test charge : polarization effects and effective potential

### G. Téllez 1, E. Trizac 2

#### Journal of Statistical Physics 146 (2012) 832-849

We study the effective interactions between a test charge Q and a one-component plasma, i.e. a complex made up of mobile point particles with charge q, and a uniform oppositely charged background. The background has the form of a flat disk, in which the mobile charges can move. The test particle is approached perpendicularly to the disk, along its axis of symmetry. All particles interact by a logarithmic potential. The long and short distance features of the effective potential --the free energy of the system for a given distance between Q and the disk-- are worked out analytically in detail. They crucially depend on the sign of Q/q, and on the global charge borne by the discotic complex, that can vanish. While most results are obtained at the intermediate coupling Gamma = beta q^2 = 2 (beta being the inverse temperature), we have also investigated situations with stronger couplings: Gamma=4 and 6. We have found that at large distances, the sign of the effective force reflects subtle details of the charge distribution on the disk, whereas at short distances, polarization effects invariably lead to effective attractions.

• 1. Departamento de Fisica,
Universidad de Los Andes
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Aging of rotational diffusion in colloidal gels and glasses

### S. Jabbari-Farouji 1, 2, G. H. Wegdam 2, Daniel Bonn 3

#### Physical Review E 86 (2012) 041401

We study the rotational diffusion of aging Laponite suspensions for a wide range of concentrations using depolarized dynamic light scattering. The measured orientational correlation functions undergo an ergodic to non-ergodic transition that is characterized by a concentration-dependent ergodicity-breaking time. We find that the relaxation times associated with rotational degree of freedom as a function of waiting time, when scaled with their ergodicity-breaking time, collapse on two distinct master curves. These master curves are similar to those previously found for the translational dynamics; The two different classes of behavior were attributed to colloidal gels and glasses. Therefore, the aging dynamics of rotational degree of freedom provides another signature of the distinct dynamical behavior of colloidal gels and glasses.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. University of Amsterdam Van der Waals-Zeeman Institute (VAN DER WAALS-ZEEMAN INSTITUTE),
University of Amsterdam
• 3. Laboratoire de Physique Statistique de l'ENS (LPS),
CNRS : UMR8550 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – Ecole Normale Supérieure de Paris - ENS Paris

• ## Application of a trace formula to the spectra of flat three-dimensional dielectric resonators

### S. Bittner 1, E. Bogomolny 2, B. Dietz 3, M. Miski-Oglu 3, A. Richter 1, 4

#### Physical Review E 85 (2012) 026203

The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the effective index of refraction approximation and a good agreement was found. It was necessary to take into account the dispersion of the effective index of refraction for the two-dimensional approximation. Furthermore, small deviations between the experimental length spectrum and the trace formula prediction were attributed to the systematic error of the effective index of refraction approximation. In summary, the methods developed in this article enable the application of the trace formula for two-dimensional dielectric resonators also to realistic, flat three-dimensional dielectric microcavities and -lasers, allowing for the interpretation of their spectra in terms of classical periodic orbits.

• 1. Institut für Kernphysik,
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Institut für Kernphysik,
• 4. ECT,
ECT

Citations to the Article (2)

• ## Arithmetic area for m planar Brownian paths

### Jean Desbois 1, Stephane Ouvry 1

#### Journal of Statistical Mechanics: Theory and Experiment (2012) P050005

We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE information, valid in the 1-path case, on the 0-winding sectors arithmetic area.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Bose-Einstein Condensation of a Gaussian Random Field in the Thermodynamic Limit

### Philippe Mounaix 1, Satya N. Majumdar 2, Abhimanyu Banerjee 3

#### Journal of Physics A: Mathematical and Theoretical 45 (2012) 115002

We derive the criterion for the Bose-Einstein condensation (BEC) of a Gaussian field $\phi$ (real or complex) in the thermodynamic limit. The field is characterized by its covariance function and the control parameter is the intensity $u=\|\phi\|_2^2/V$, where $V$ is the volume of the box containing the field. We show that for any dimension $d$ (including $d=1$), there is a class of covariance functions for which $\phi$ exhibits a BEC as $u$ is increased through a critical value $u_c$. In this case, we investigate the probability distribution of the part of $u$ contained in the condensate. We show that depending on the parameters characterizing the covariance function and the dimension $d$, there can be two distinct types of condensate: a Gaussian distributed 'normal' condensate with fluctuations scaling as $1/\sqrt{V}$, and a non Gaussian distributed 'anomalous' condensate. A detailed analysis of the anomalous condensate is performed for a one-dimensional system ($d=1$). Extending this one-dimensional analysis to exactly the point of transition between normal and anomalous condensations, we find that the condensate at the transition point is still Gaussian distributed but with anomalously large fluctuations scaling as $\sqrt{\ln(L)/L}$, where $L$ is the system length. The conditional spectral density of $\phi$, knowing $u$, is given for all the regimes (with and without BEC).

• 1. Centre de Physique Théorique (CPHT),
CNRS : UMR7644 – Polytechnique - X
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Indian Institute of Technology [Kanpur] (IIT Kanpur),
Indian Institute of Technology Kanpur

• ## Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions?

### Alan Gabel 1, Satya N. Majumdar 2, Nagendra K. Panduranga 1, S. Redner 1

#### Journal of Statistical Mechanics: Theory and Experiment (2012) P05011

We study the survival of a single diffusing lamb on the positive half line in the presence of N diffusing lions that all start at the same position L to the right of the lamb and a haven at x=0. If the lamb reaches this haven before meeting any lion, the lamb survives. We investigate the survival probability of the lamb, S_N(x,L), as a function of N and the respective initial positions of the lamb and the lions, x and L. We determine S_N(x,L) analytically for the special cases of N=1 and N--->oo. For large but finite N, we determine the unusual asymptotic form whose leading behavior is S_N(z)\simN^{-z^2}, with z=x/L. Simulations of the capture process very slowly converge to this asymptotic prediction as N reaches 10^{500}.

• 1. Center for Polymer Studies (CPS),
Boston University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Casimir forces beyond the proximity approximation

### G. Bimonte 1, T. Emig 2, R. L. Jaffe 3, M. Kardar 4

#### Europhycs Letters 97 (2012) 50001

The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Padé extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere-plate Casimir force at all separations.

• 1. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli (INFN, Sezione di Napoli),
INFN
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Department of Physics, Center for Theoretical Physics,
Massachussetts Institute of Technology (MIT)
• 4. Department of Physics,
Massachusetts Institute of Technology

• ## Casimir interaction between inclined metallic cylinders

### P. Rodriguez-Lopez 1, T. Emig 2

#### Physical Review A 85 (2012) 032510

The Casimir interaction between one-dimensional metallic objects (cylinders, wires) displays unconventional features. Here we study the orientation dependence of this interaction by computing the Casimir energy between two inclined cylinders over a wide range of separations. We consider Dirichlet, Neumann and perfect metal boundary conditions, both at zero temperature and in the classical high temperature limit. For all types of boundary conditions, we find that at large distances the interaction decays slowly with distance, similarly to the case of parallel cylinders, and at small distances scales as the interaction of two spheres (but with different numerical coefficients). Our numerical results at intermediate distances agree with our analytic predictions at small and large separations. Experimental implications are discussed.

• 1. Departamento de Fisica Aplicada,
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Collective charge fluctuations and Casimir interactions for quasi one-dimensional metals

### Ehsan Noruzifar 1, Thorsten Emig 2, Umar Mohideen 1, Roya Zandi 1

#### Physical Review B 86 (2012) 115449

We investigate the Casimir interaction between two parallel metallic cylinders and between a metallic cylinder and plate. The material properties of the metallic objects are implemented by the plasma, Drude and perfect metal model dielectric functions. We calculate the Casimir interaction numerically at all separation distances and analytically at large separations. The large-distance asymptotic interaction between one plasma cylinder parallel to another plasma cylinder or plate does not depend on the material properties, but for a Drude cylinder it depends on the dc conductivity $\sigma$. At intermediate separations, for plasma cylinders the asymptotic interaction depends on the plasma wave length $\lambda_{\rm p}$ while for Drude cylinders the Casimir interaction can become independent of the material properties. We confirm the analytical results by the numerics and show that at short separations, the numerical results approach the proximity force approximation.

• 1. Department of Physics and Astronomy,
University of California, Riverside
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (1)

• ## Compressed Sensing of Approximately-Sparse Signals: Phase Transitions and Optimal Reconstruction

### Jean Barbier 1, Florent Krzakala 1, Marc Mézard 2, Lenka Zdeborová 3

#### 50th annual Allerton conference on communication, control, and computing, États-Unis (2012)

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large) components the other components are not strictly equal to zero, but are only close to zero. In this paper we model the approximately sparse signal with a Gaussian distribution of small components, and we study its compressed sensing with dense random matrices. We use replica calculations to determine the mean-squared error of the Bayes-optimal reconstruction for such signals, as a function of the variance of the small components, the density of large components and the measurement rate. We then use the G-AMP algorithm and we quantify the region of parameters for which this algorithm achieves optimality (for large systems). Finally, we show that in the region where the GAMP for the homogeneous measurement matrices is not optimal, a special "seeding" design of a spatially-coupled measurement matrix allows to restore optimality.

• 1 : Laboratoire de Physico-Chimie Théorique (LPCT)
CNRS : UMR7083 – ESPCI ParisTech
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3 : Institut de Physique Théorique (ex SPhT) (IPHT)
CNRS : URA2306 – CEA : DSM/IPHT

• ## Controlling integrability in a quasi-1D atom-dimer mixture

### D. S. Petrov 1, 2, V. Lebedev 3, J. T. M. Walraven 3

#### Physical Review A 85 (2012) 062711

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length l_0 of the transverse confinement is smaller than the dimer size, ~l_0^2/|a|, where a<0 is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to a^6 in the bosonic case and to a^8 for the up-(up-down) scattering in a two-component fermionic mixture. We show that by tuning a and l_0 one can control the 'degree of integrability' in a quasi-1D atom-dimer mixture in an extremely wide range leaving thermodynamic quantities unchanged. We find that the relaxation to deeply bound states in the fermionic (bosonic) case is slower (faster) than transitions between different Bethe ansatz states. We propose a realistic experiment for detailed studies of the crossover from integrable to nonintegrable dynamics.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. National Research Centre "Kurchatov Institute" (NRC KI),
University of Moscow
• 3. Van der Waals-Zeeman Institute,
University of Amsterdam

Citations to the Article (1)

• ## Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal $1/f$ noise

### Yan V. Fyodorov, Pierre Le Doussal, Alberto Rosso

#### Journal of Statistical Physics 149 (2012) 898-920

To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By employing the thermodynamic formalism we predict the characteristic scale and the precise scaling form of the distribution of number of points above a given level. We demonstrate that the powerlaw forward tail of the probability density, with exponent controlled by the level, results in an important difference between the mean and the typical values of the counting function. This can be further used to determine the typical threshold $x_m$ of extreme values in the pattern which turns out to be given by $x_m^{(typ)}=2-c\ln{\ln{M}}/\ln{M}$ with $c=3/2$. Such observation provides a rather compelling explanation of the mechanism behind universality of $c$. Revealed mechanisms are conjectured to retain their qualitative validity for a broad class of disorder-generated multifractal fields. In particular, we predict that the typical value of the maximum $p_{max}$ of intensity is to be given by $-\ln{p_{max}} = \alpha_{-}\ln{M} + \frac{3}{2f'(\alpha_{-})}\ln{\ln{M}} + O(1)$, where $f(\alpha)$ is the corresponding singularity spectrum vanishing at $\alpha=\alpha_{-}>0$. For the $1/f$ noise we also derive exact as well as well-controlled approximate formulas for the mean and the variance of the counting function without recourse to the thermodynamic formalism.

• ## Critical phenomena and phase sequence in classical bilayer Wigner crystal at zero temperature

### L. Samaj 1, E. Trizac 1

#### Physical Review B (Condensed Matter) 85 (2012) 205131

We study the ground-state properties of a system of identical classical Coulombic point particles, evenly distributed between two equivalently charged parallel plates at distance $d$; the system as a whole is electroneutral. It was previously shown that upon increasing d from 0 to infinity, five different structures of the bilayer Wigner crystal become energetically favored, starting from a hexagonal lattice (phase I, d=0) and ending at a staggered hexagonal lattice (phase V, d -> infinity). In this paper, we derive new series representations of the ground-state energy for all five bilayer structures. The derivation is based on a sequence of transformations for lattice sums of Coulomb two-particle potentials plus the neutralizing background, having their origin in the general theory of Jacobi theta functions. The new series provide convenient starting points for both analytical and numerical progress. Its convergence properties are indeed excellent: Truncation at the fourth term determines in general the energy correctly up to 17 decimal digits. The accurate series representations are used to improve the specification of transition points between the phases and to solve a controversy in previous studies. In particular, it is shown both analytically and numerically that the hexagonal phase I is stable only at d=0, and not in a finite interval of small distances between the plates as was anticipated before. The expansions of the structure energies around second-order transition points can be done analytically, which enables us to show that the critical behavior is of the Ginzburg-Landau type, with a mean-field critical index beta=1/2 for the growth of the order parameters.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Dissipative homogeneous Maxwell mixtures: ordering transition in the tracer limit

### V. Garzó 1, E. Trizac 2

#### Granular Matter 14 (2012) 99

The homogeneous Boltzmann equation for inelastic Maxwell mixtures is considered to study the dynamics of tracer particles or impurities (solvent) immersed in a uniform granular gas (solute). The analysis is based on exact results derived for a granular binary mixture in the homogeneous cooling state (HCS) that apply for arbitrary values of the parameters of the mixture (particle masses $m_i$, mole fractions $c_i$, and coefficients of restitution $\alpha_{ij}$). In the tracer limit ($c_1\to 0$), it is shown that the HCS supports two distinct phases that are evidenced by the corresponding value of $E_1/E$, the relative contribution of the tracer species to the total energy. Defining the mass ratio $\mu = m_1/m_2$, there indeed exist two critical values $\mu_\text{HCS}^{(-)}$ and $\mu_\text{HCS}^{(+)}$ (which depend on the coefficients of restitution), such that $E_1/E=0$ for $\mu_\text{HCS}^{(-)}<\mu<\mu_\text{HCS}^{(+)}$ (disordered or normal phase), while $E_1/E\neq 0$ for $\mu<\mu_\text{HCS}^{(-)}$ and/or $\mu>\mu_\text{HCS}^{(+)}$ (ordered phase).

• 1. Departamento de Fisica,
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Dynamic Monte Carlo Simulations of Anisotropic Colloids

### Sara Jabbari-Farouji 1, Emmanuel Trizac 1

#### Journal of Chemical Physics 137 (2012) 054107

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach --discarding hydrodynamics interactions-- first allows us to improve the efficiency of previous Dynamic Monte Carlo algorithms for spherical Brownian particles. In a second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Dynamical heterogeneity in aging colloidal glasses of Laponite

### Sara Jabbari-Farouji 1, 2, Rojman Zargar 2, Gerard Wegdam 2, Daniel Bonn 3, 4

#### Soft Matter 8 (2012) 5507-5512

Glasses behave as solids due to their long relaxation time; however the origin of this slow response remains a puzzle. Growing dynamic length scales due to cooperative motion of particles are believed to be central to the understanding of both the slow dynamics and the emergence of rigidity. Here, we provide experimental evidence of a growing dynamical heterogeneity length scale that increases with increasing waiting time in an aging colloidal glass of Laponite. The signature of heterogeneity in the dynamics follows from dynamic light scattering measurements in which we study both the rotational and translational diffusion of the disk-shaped particles of Laponite in suspension. These measurements are accompanied by simultaneous microrheology and macroscopic rheology experiments. We find that rotational diffusion of particles slows down at a faster rate than their translational motion. Such decoupling of translational and orientational degrees of freedom finds its origin in the dynamic heterogeneity since rotation and translation probe different length scales in the sample. The macroscopic rheology experiments show that the low frequency shear viscosity increases at a much faster rate than both rotational and translational diffusive relaxation times.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Van der Waals-Zeeman Institute,
University of Amsterdam
• 3. University of Amsterdam Van der Waals-Zeeman Institute (VAN DER WAALS-ZEEMAN INSTITUTE),
University of Amsterdam
• 4. Laboratoire de Physique Statistique de l'ENS (LPS),
CNRS : UMR8550 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – Ecole Normale Supérieure de Paris - ENS Paris

Citations to the Article (1)

• ## Dynamics of a massive intruder in a homogeneously driven granular fluid

### A. Puglisi 1, A. Sarracino 2, G. Gradenigo 3, D. Villamaina 4

#### Granular Matter 14 (2012) 235-238

A massive intruder in a homogeneously driven granular fluid, in dilute configurations, performs a memory-less Brownian motion with drag and temperature simply related to the average density and temperature of the fluid. At volume fraction $\sim 10-50%$ the intruder's velocity correlates with the local fluid velocity field: such situation is approximately described by a system of coupled linear Langevin equations equivalent to a generalized Brownian motion with memory. Here one may verify the breakdown of the Fluctuation-Dissipation relation and the presence of a net entropy flux - from the fluid to the intruder - whose fluctuations satisfy the Fluctuation Relation.

• 1. Dipartimento di Fisica,
Università La Sapienza
• 2. Dipartimento di Fisica,
CNR - Consiglio Nationale delle Ricerche
• 3. Dipartimento di Fisica,
CNR - Consiglio Nationale delle Ricerche
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Edge properties of principal fractional quantum Hall states in the cylinder geometry

### Paul Soulé 1, Thierry Jolicoeur 1

#### Physical Review B (Condensed Matter) 86 (2012) 115214

We study fractional quantum Hall states in the cylinder geometry with open boundaries. We focus on principal fermionic 1/3 and bosonic 1/2 fractions in the case of hard-core interactions. The gap behavior as a function of the cylinder radius is analyzed. By adding enough orbitals to allow for edge modes we show that it is possible to measure the Luttinger parameter of the non-chiral liquid formed by the combination of the two counterpropagating edges when we add a small confining potential. While we measure a Luttinger exponent consistent with the chiral Luttinger theory prediction for the full hard-core interaction, the exponent remains non-trivial in the Tao-Thouless limit as well as for simple truncated states that can be constructed on the cylinder. If the radius of the cylinder is taken to infinity the problem becomes a Tonks-Girardeau one-dimensional interacting gas in Fermi and Bose cases. Finally we show that the the Tao-Thouless and truncated states have an edge electron propagator which decays spatially with a Fermi-liquid exponent even if the energy spectrum can still be described by a non-trivial Luttinger parameter.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Effect of coupling asymmetry on mean-field solutions of direct and inverse Sherrington-Kirkpatrick model

### Jason Sakellariou 1, Yasser Roudi 2, 3, Marc Mezard 1, John Hertz 4, 5

#### Philosophical Magazine 92 (2012) 272-279

We study how the degree of symmetry in the couplings influences the performance of three mean field methods used for solving the direct and inverse problems for generalized Sherrington-Kirkpatrick models. In this context, the direct problem is predicting the potentially time-varying magnetizations. The three theories include the first and second order Plefka expansions, referred to as naive mean field (nMF) and TAP, respectively, and a mean field theory which is exact for fully asymmetric couplings. We call the last of these simply MF theory. We show that for the direct problem, nMF performs worse than the other two approximations, TAP outperforms MF when the coupling matrix is nearly symmetric, while MF works better when it is strongly asymmetric. For the inverse problem, MF performs better than both TAP and nMF, although an ad hoc adjustment of TAP can make it comparable to MF. For high temperatures the performance of TAP and MF approach each other.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Kavli Institute for Systems Neuroscience,
Kavli Institute for Systems Neuroscience
• 3. NORDITA,
NORDITA
• 4. NORDITA,
NORDITA
• 5. Niels Bohr Institute (NBI),
Niels Bohr Institute

• ## Einstein relation in superdiffusive systems

### Giacomo Gradenigo 1, Alessandro Sarracino 1, Dario Villamaina 2, Angelo Vulpiani 3

#### Journal of Statistical Mechanics: Theory and Experiment (2012) L06001

We study the Einstein relation between diffusion and response to an external field in systems showing superdiffusion. In particular, we investigate a continuous time Levy walk where the velocity remains constant for a time \tau, with distribution P(\tau) \tau^{-g}. At varying g the diffusion can be standard or anomalous; in spite of this, if in the unperturbed system a current is absent, the Einstein relation holds. In the case where a current is present the scenario is more complicated and the usual Einstein relation fails. This suggests that the main ingredient for the breaking of the Einstein relation is not the anomalous diffusion but the presence of a mean drift (current).

• 1. Istituto dei Sistemi Complessi--CNR,
Università Sapienza
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Dipartimento di Fisica,
Università Sapienza

• ## Electron and nuclear spin dynamics in the thermal mixing model of dynamic nuclear polarization

### Sonia Colombo Serra 1, Alberto Rosso 2, Fabio Tedoldi 1

#### Physical Chemistry Chemical Physics 14 (2012) 13299-13308

A novel mathematical treatment is proposed for computing the time evolution of dynamic nuclear polarization processes in the low temperature thermal mixing regime. Without assuming any a priori analytical form for the electron polarization, our approach provides a quantitative picture of the steady state that recovers the well known Borghini prediction based on thermodynamics arguments, as long as the electrons-nuclei transition rates are fast compared to the other relevant time scales. Substantially different final polarization levels are achieved instead when the latter assumption is relaxed in the presence of a nuclear leakage term, even though very weak, suggesting a possible explanation for the deviation between the measured steady state polarizations and the Borghini prediction. The proposed methodology also allows to calculate nuclear polarization and relaxation times, once specified the electrons/nuclei concentration ratio and the typical rates of the microscopic processes involving the two spin species. Numerical results are shown to account for the manifold dynamical behaviours of typical DNP samples.

• 1. Centro Ricerche Bracco,
Centro Ricerche Bracco
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (1)

• ## Entangling many-body bound states with propagative modes in Bose-Hubbard systems

### Mario Collura 1, Helge Aufderheide 2, Guillaume Roux 3, Dragi Karevski 1

#### Physical Review A 86 (2012) 013615

The quantum evolution of a cloud of bosons initially localized on part of a one dimensional optical lattice and suddenly subjected to a linear ramp is studied, realizing a quantum analog of the 'Galileo ramp' experiment. The main remarkable effects of this realistic setup are revealed using analytical and numerical methods. Only part of the particles are ejected for a high enough ramp, while the others remain self-trapped. Then, the trapped density profile displays rich dynamics with Josephson-like oscillations around a plateau. This setup, by coupling bound states to propagative modes, creates two diverging condensates for which the entanglement is computed and related to the equilibrium one. Further, we address the role of integrability on the entanglement and on the damping and thermalization of simple observables.

• 1. Institut Jean Lamour : Matériaux -Métallurgie - Nanosciences - Plasma - Surfaces (IJL),
Université Henri Poincaré - Nancy I – CNRS : UMR7198 – Institut National Polytechnique de Lorraine (INPL) – Université Paul Verlaine - Metz
• 2. Department Biological Physics,
Max-Planck-Institute
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (1)

• ## Equilibrium strategy and population-size effects in lowest unique bid auctions

### Simone Pigolotti 1, 2, Sebastian Bernhardsson 1, 3, Jeppe Juul 1, Gorm Galster 1, Pierpaolo Vivo 4

#### Physical Review Letters 108 (2012) 088701

In lowest unique bid auctions, $N$ players bid for an item. The winner is whoever places the \emph{lowest} bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large dataset of internet auctions. The theory agrees with the data with striking accuracy for small population size $N$, while for larger $N$ a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.

• 1. Niels Bohr Institute (NBI),
Niels Bohr Institute
• 2. Dept. de Fisica i Eng. Nuclear,
Universitat Politécnica de Catalunya
• 3. Swedish Defence Research Agency,
Swedish Defence Research Agency
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane geometry

### G. Bimonte 1, T. Emig 2

#### Physical Review Letters 109 (2012) 160403

Analytic expressions that describe Casimir interactions over the entire range of separations have been limited to planar surfaces. Here we derive analytic expressions for the classical or high-temperature limit of Casimir interactions between two spheres (interior and exterior configurations), including the sphere-plane geometry as a special case, using bispherical coordinates. We consider both Dirichlet boundary conditions and metallic boundary conditions described by the Drude model. At short distances, closed-form expansions are derived from the exact result, displaying an intricate structure of deviations from the commonly employed proximity force approximation.

• 1. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli (INFN, Sezione di Napoli),
INFN
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Exact wavefunctions for excitations of the nu=1/3 fractional quantum Hall state from a model Hamiltonian

### Paul Soulé 1, Thierry Jolicoeur 1

#### Physical Review B (Condensed Matter) 85 (2012) 155116

We study fractional quantum Hall states in the cylinder geometry with open boundaries. By truncating the Coulomb interactions between electrons we show that it is possible to construct infinitely many exact eigenstates including the ground state, quasiholes, quasielectrons and the magnetoroton branch of excited states.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Feshbach resonances in Cesium at Ultra-low Static Magnetic Fields

### D. J. Papoular 1, 2, S. Bize 3, A. Clairon 3, H. Marion 3, S. J. Kokkelmans 4, G. V. Shlyapnikov 1, 5

#### Physical Review A 86 (2012) 040701

We have observed Feshbach resonances for 133Cs atoms in two different hyperfine states at ultra-low static magnetic fields by using an atomic fountain clock. The extreme sensitivity of our setup allows for high signal-to-noise-ratio observations at densities of only 2*10^7 cm^{-3}. We have reproduced these resonances using coupled-channels calculations which are in excellent agreement with our measurements. We justify that these are s-wave resonances involving weakly-bound states of the triplet molecular Hamiltonian, identify the resonant closed channels, and explain the observed multi-peak structure. We also describe a model which precisely accounts for the collisional processes in the fountain and which explains the asymmetric shape of the observed Feshbach resonances in the regime where the kinetic energy dominates over the coupling strength.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Dipartimento di Fisica,
Universita Trento
• 3. Systèmes de Référence Temps Espace (SYRTE),
CNRS : UMR8630 – INSU – Observatoire de Paris – Université Paris VI - Pierre et Marie Curie
• 4. Department of Physics,
Eindhoven University of Technology
• 5. Van der Waals-Zeeman Institute,
University of Amsterdam

• ## Field induced stationary state for an accelerated tracer in a bath

### Matthieu Barbier 1, Emmanuel Trizac 1

#### Journal of Statistical Physics 149 (2012) 317-341

Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results --mostly derived for a one dimensional system-- are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large -v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## From Weak- to Strong-Coupling Mesoscopic Fermi Liquids

### Dong E. Liu 1, Sébastien Burdin 2, Harold U. Baranger 1, Denis Ullmo 3

#### EPL 97 (2012) 17006

We study mesoscopic fluctuations in a system in which there is a continuous connection between two distinct Fermi liquids, asking whether the mesoscopic variation in the two limits is correlated. The particular system studied is an Anderson impurity coupled to a finite mesoscopic reservoir described by random matrix theory, a structure which can be realized using quantum dots. We use the slave boson mean field approach to connect the levels of the uncoupled system to those of the strong coupling Noziéres Fermi liquid. We find strong but not complete correlation between the mesoscopic properties in the two limits and several universal features.

• 1. Duke Physics,
Duke University
• 2. Laboratoire Ondes et Matière d'Aquitaine (LOMA),
CNRS : UMR5798
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (3)

• ## Generation of dispersive shock waves by the flow of a Bose-Einstein condensate past a narrow obstacle

### A. M. Kamchatnov 1, N. Pavloff 2

#### Physical Review A 85 (2012) 033603

We study the flow of a quasi-one-dimensional Bose-Einstein condensate incident onto a narrow obstacle. We consider a configuration in which a dispersive shock is formed and propagates upstream away from the obstacle while the downstream flow reaches a supersonic velocity, generating a sonic horizon. Conditions for obtaining this regime are explicitly derived and the accuracy of our analytical results is confirmed by numerical simulations.

• 1. Institute of Spectroscopy,
Russian Academy of Sciences
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (7)

• ## Ground state of classical bilayer Wigner crystals

### L. Samaj 1, 2, E. Trizac 2

#### Europhysics Letters 98 (2012) 36004

We study the ground state structure of electronic-like bilayers, where different phases compete upon changing the inter-layer separation or particle density. New series representations with exceptional convergence properties are derived for the exact Coulombic energies under scrutiny. The complete phase transition scenario --including critical phenomena-- can subsequently be worked out in detail, thereby unifying a rather scattered or contradictory body of literature, hitherto plagued by the inaccuracies inherent to long range interaction potentials.

• 1. Institute of Physics,
Slovak Academy of Sciences
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Impurity in a sheared inelastic Maxwell gas

### V. Garzó 1, E. Trizac 2

#### Physical Review E 85 (2012) 011302

The Boltzmann equation for inelastic Maxwell models is considered in order to investigate the dynamics of an impurity (or intruder) immersed in a granular gas driven by a uniform shear flow. The analysis is based on an exact solution of the Boltzmann equation for a granular binary mixture. It applies for conditions arbitrarily far from equilibrium (arbitrary values of the shear rate $a$) and for arbitrary values of the parameters of the mixture (particle masses $m_i$, mole fractions $x_i$, and coefficients of restitution $\alpha_{ij}$). In the tracer limit where the mole fraction of the intruder species vanishes, a non equilibrium phase transition takes place. We thereby identity ordered phases where the intruder bears a finite contribution to the properties of the mixture, in a region of parameter space that is worked out in detail. These findings extend previous results obtained for ordinary Maxwell gases, and further show that dissipation leads to new ordered phases.

• 1. Departamento de Fisica,
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Lane formation in a lattice model for oppositely driven binary particles

### Hiroki Ohta 1

#### Europhysics Letters 99 (2012) 40006

Oppositely driven binary particles with repulsive interactions on the square lattice are investigated at the zero-temperature limit. Two classes of steady states related to stuck configurations and lane formations have been constructed in systematic ways under certain conditions. A mean-field type analysis carried out using a percolation problem based on the constructed steady states provides an estimation of the phase diagram, which is qualitatively consistent with numerical simulations. Further, finite size effects in terms of lane formations are discussed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs

### Emilio Cuevas, Mikhail Feigel'man, Lev Ioffe, Marc Mezard

#### Nature Communications 3 (2012) 1128

The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. While small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce thermal bath and excitation decay. This intrinsic decoherence is manifested by a broadening of energy levels which aquire a finite width. The important question is what is the driving force and the mechanism of transition(s) between two different types of many-body systems - with and without intrinsic decoherence? Here we address this question via the numerical study of energy level statistics of a system of spins-1/2 with anisotropic exchange interactions and random transverse fields. Our results present the first evidence for a well-defined quantum phase transition between domains of discrete and continous many-body spectra in a class of random spin models. Because this model also describes the physics of the superconductor-insulator transition in disordered superconductors like InO and similar materials, our results imply the appearance of novel insulating phases in the vicinity of this transition

• ## Material dependence of Casimir forces: gradient expansion beyond proximity

### G. Bimonte 1, T. Emig 2, M. Kardar 3

#### Applied Physics Letters 100 (2012) 074110

A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) and insulators (SiO$_2$) at room temperature. We derive an explicit expression for the amplitude $\hat\theta_1$ of the PFA correction to the force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the Casimir free energy are found to scale logarithmically with distance. For gold, $\hat\theta_1$ has an unusually large temperature dependence.

• 1. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli (INFN, Sezione di Napoli),
INFN
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Department of Physics,
Massachusetts Institute of Technology

• ## Mesoscopic Anderson Box: Connecting Weak to Strong Coupling

### Sébastien Burdin 2, Harold U. Baranger 1, Denis Ullmo 3

#### Physical Review B 85, 15 (2012) 155455

Both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. In an Anderson box, mesoscopic fluctuations of the effective single particle properties will be large. We study how the statistical fluctuations at low temperature in these two problems are connected, using random matrix theory and the slave boson mean field approximation (SBMFA). First, for a resonant level model such as results from the SBMFA, we find the joint distribution of energy levels with and without the resonant level present. Second, if only energy levels within the Kondo resonance are considered, the distributions of perturbed levels collapse to universal forms for both orthogonal and unitary ensembles for all values of the coupling. These universal curves are described well by a simple Wigner-surmise type toy model. Third, we study the fluctuations of the mean field parameters in the SBMFA, finding that they are small. Finally, the change in the intensity of an eigenfunction at an arbitrary point is studied, such as is relevant in conductance measurements: we find that the introduction of the strongly-coupled impurity considerably changes the wave function but that a substantial correlation remains.

• 1. Duke Physics,
Duke University
• 2. Laboratoire Ondes et Matière d'Aquitaine (LOMA),
CNRS : UMR5798
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (1)

• ## Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime

### E. Bogomolny 1, O. Giraud 1

#### Physical Review E 85 (2012) 046208

We construct perturbation series for the q-th moment of eigenfunctions of various critical random matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the region q<1/2. Our findings allow to verify, at first leading orders in the strong multifractality limit, the symmetry relation for anomalous fractal dimensions Delta(q)=Delta(1-q), recently conjectured for critical models where an analogue of the metal-insulator transition takes place. It is known that this relation is verified at leading order in the weak multifractality regime. Our results thus indicate that this symmetry holds in both limits of small and large coupling constant. For general values of the coupling constant we present careful numerical verifications of this symmetry relation for different critical random matrix ensembles. We also present an example of a system closely related to one of these critical ensembles, but where the symmetry relation, at least numerically, is not fulfilled.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Multifractality of eigenfunctions in spin chains

### Yasar Yilmaz Atas 1, Eugene Bogomolny 1

#### Physical Review E 86 (2012) 021104

We investigate different one-dimensional quantum spin-1/2 chain models and by combining analytical and numerical calculations prove that their ground state wave functions in the natural spin basis are multifractals with, in general, non-trivial fractal dimensions.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Multifractality of quantum wave packets

### Ignacio Garcia-Mata 1, 2, J. Martin 3, Olivier Giraud 4, Bertrand Georgeot 1

#### Physical Review E86 (2012) 056215

We study a version of the mathematical Ruijsenaars-Schneider model, and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets, and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, different from the mulifractality of eigenvectors, but related to it, as is the rate of the decrease. Our results are relevant to experimental situations.

• 1 : Laboratoire de Physique Théorique - IRSAMC (LPT)
CNRS : UMR5152 – Université Paul Sabatier (UPS) - Toulouse III
• 2 : Instituto de Investigaciones F'ısicas de Mar del Plata (IFIMAR)
Univ. Nacional de La Plata and Conicet
• 3 : Institut de Physique Nucl'eaire, Atomique et de Spectroscopie
Université de Liège
• 4 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## New alphabet-dependent morphological transition in a random RNA alignment

### O. V. Valba 1, 2, M. V. Tamm 3, S. K. Nechaev 1, 4

#### Physical Review Letters 109 (2012) 018102

We study the fraction $f$ of nucleotides involved in the formation of a cactus--like secondary structure of random heteropolymer RNA--like molecules. In the low--temperature limit we study this fraction as a function of the number $c$ of different nucleotide species. We show, that with changing $c$, the secondary structures of random RNAs undergo a morphological transition: $f(c)\to 1$ for $c \le c_{\rm cr}$ as the chain length $n$ goes to infinity, signaling the formation of a virtually 'perfect' gapless secondary structure; while $f(c)<1$ for $c>c_{\rm cr}$, what means that a non-perfect structure with gaps is formed. The strict upper and lower bounds $2 \le c_{\rm cr} \le 4$ are proven, and the numerical evidence for $c_{\rm cr}$ is presented. The relevance of the transition from the evolutional point of view is discussed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Moscow Institute of Physics and Technology (MIPT),
Moscow Institute of Physics and Technology
• 3. Physics Department,
Moscow State University
• 4. P. N. Lebedev Physical Institute,
Russian Academy of Science

• ## Non-equilibrium and information: the role of cross-correlations

### Andrea Crisanti 1, Andrea Puglisi 2, Dario Villamaina 3

#### Physical Review E 85 (2012) 061127

We discuss the relevance of information contained in cross-correlations among different degrees of freedom, which is crucial in non-equilibrium systems. In particular we consider a stochastic system where two degrees of freedom $X_1$ and $X_2$ - in contact with two different thermostats - are coupled together. The production of entropy and the violation of equilibrium fluctuation-dissipation theorem (FDT) are both related to the cross-correlation between $X_1$ and $X_2$. Information about such cross-correlation may be lost when single-variable reduced models, for $X_1$, are considered. Two different procedures are typically applied: (a) one totally ignores the coupling with $X_2$; (b) one models the effect of $X_2$ as an average memory effect, obtaining a generalized Langevin equation. In case (a) discrepancies between the system and the model appear both in entropy production and linear response; the latter can be exploited to define effective temperatures, but those are meaningful only when time-scales are well separated. In case (b) linear response of the model well reproduces that of the system; however the loss of information is reflected in a loss of entropy production. When only linear forces are present, such a reduction is dramatic and makes the average entropy production vanish, posing problems in interpreting FDT violations.

• 1. Sapienza,
Sapienza
• 2. Dipartimento di Fisica (DF-LS),
Università degli studi di Roma I - La Sapienza
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Novel Fermi Liquid of 2D Polar Molecules

### Zhen-Kai Lu 1, 2, 3, G. V. Shlyapnikov 1, 4

#### Physical Review A 85 (2012) 023614

We study Fermi liquid properties of a weakly interacting 2D gas of single-component fermionic polar molecules with dipole moments $d$ oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as $1/r^3$ at large distances $r$, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter $k_Fr_*$, where $k_F$ is the Fermi momentum, and $r_*=md^2/\hbar^2$ is the dipole-dipole length, with $m$ being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in $k_Fr_*$ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, like it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Max Planck Institute für quantenoptik,
Max Planck Institute
• 3. Fédération de recherche du département de physique de l'Ecole Normale Supérieure (FRDPENS),
CNRS : FR684 – Ecole Normale Supérieure de Paris - ENS Paris
• 4. Van der Waals-Zeeman Institute,
University of Amsterdam

Citations to the Article (8)

• ## Number of Common Sites Visited by N Random Walkers

### Satya N. Majumdar 1, Mikhail V. Tamm 2

#### Physical Review E 86 (2012) 021135

We compute analytically the mean number of common sites, W_N(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N-d) plane, there are three distinct regimes for the asymptotic large t growth of W_N(t). These three regimes are separated by two critical lines d=2 and d=d_c(N)=2N/(N-1) in the (N-d) plane. For d<2, W_N(t)\sim t^{d/2} for large t (the N dependence is only in the prefactor). For 2

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Department of Physics,
Lomonosov State University

• ## Number of relevant directions in Principal Component Analysis and Wishart random matrices

### Satya N. Majumdar 1, Pierpaolo Vivo 1

#### Physical Review Letters 108 (2012) 200601

We compute analytically, for large $N$, the probability $\mathcal{P}(N_+,N)$ that a $N\times N$ Wishart random matrix has $N_+$ eigenvalues exceeding a threshold $N\zeta$, including its large deviation tails. This probability plays a benchmark role when performing the Principal Component Analysis of a large empirical dataset. We find that $\mathcal{P}(N_+,N)\approx\exp(-\beta N^2 \psi_\zeta(N_+/N))$, where $\beta$ is the Dyson index of the ensemble and $\psi_\zeta(\kappa)$ is a rate function that we compute explicitly in the full range $0\leq \kappa\leq 1$ and for any $\zeta$. The rate function $\psi_\zeta(\kappa)$ displays a quadratic behavior modulated by a logarithmic singularity close to its minimum $\kappa^\star(\zeta)$. This is shown to be a consequence of a phase transition in an associated Coulomb gas problem. The variance $\Delta(N)$ of the number of relevant components is also shown to grow universally (independent of $\zeta)$ as $\Delta(N)\sim (\beta \pi^2)^{-1}\ln N$ for large $N$.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## On the joint distribution of the maximum and its position of the Airy2 process minus a parabola

### Jinho Baik 1, Karl Liechty 1, Gregory Schehr 2

#### Journal of Mathematical Physics 53 (2012) 083303

The maximal point of the Airy2 process minus a parabola is believed to describe the scaling limit of the end-point of the directed polymer in a random medium, which was proved to be true for a few specific cases. Recently two different formulas for the joint distribution of the location and the height of this maximal point were obtained, one by Moreno Flores, Quastel and Remenik, and the other by Schehr. The first formula is given in terms of the Airy function and an associated operator, and the second formula is expressed in terms of the Lax pair equations of the Painleve II equation. We give a direct proof that these two formulas are the same.

• 1. Department of Mathematics,
Michigan State University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers

### Christophe Texier 1, 2

#### Physica Scripta 86 (2012) 058515

Some results on the ordered statistics of eigenvalues for one-dimensional random Schrödinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces eigenvalue correlations and makes the ordered statistics problem nontrivial. The resulting distributions are used to analyze the problem of classical diffusion in a random force field (Sinai problem) in the presence of weakly concentrated absorbers. It is shown that the slowly decaying averaged return probability of the Sinai problem, $\mean{P(x,t|x,0)}\sim \ln^{-2}t$, is converted into a power law decay, $\mean{P(x,t|x,0)}\sim t^{-\sqrt{2\rho/g}}$, where $g$ is the strength of the random force field and $\rho$ the density of absorbers.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique des Solides (LPS),
CNRS : UMR8502 – Université Paris XI - Paris Sud

• ## Parametrization of spin-1 classical states

### Olivier Giraud 1, Petr Braun 2, 3, Daniel Braun 4

#### Physical Review A 85 (2012) 032101

We give an explicit parametrization of the set of mixed quantum states and of the set of mixed classical states for a spin--1. Classical states are defined as states with a positive Glauber-Sudarshan P-function. They are at the same time the separable symmetric states of two qubits. We explore the geometry of this set, and show that its boundary consists of a two-parameter family of ellipsoids. The boundary does not contain any facets, but includes straight-lines corresponding to mixtures of pure classical states.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institute of Physics, Saint-Petersburg University,
Saint-Petersburg University
• 3. Fachbereich Physik, Universitaet Duisburg-Essen,
Universitaet Duisburg-Essen
• 4. Laboratoire de Physique Théorique - IRSAMC (LPT),
CNRS : UMR5152 – Université Paul Sabatier - Toulouse III

• ## Phase behaviour of colloidal assemblies on 2D corrugated substrates

### Samir El Shawish 1, Emmanuel Trizac 2, Jure Dobnikar 1

#### Journal of Physics: Condensed Matter 24 (2012) 284118

We investigate - with Monte Carlo computer simulations - the phase behaviour of dimeric colloidal molecules on periodic substrates with square symmetry. The molecules are formed in a two-dimensional suspension of like charged colloids subject to periodic external confinement, which can be experimentally realized by optical methods. We study the evolution of positional and orientational order by varying the temperature across the melting transition. We propose and evaluate appropriate order parameters as well as the specific heat capacity and show that the decay of positional correlations belongs to a class of crossover transitions while the orientational melting is a second-order phase transition.

• 1. Jozef Stefan Institute,
Jozef Stefan Institute
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices

### Florent Krzakala 1, Marc Mézard 2, François Sausset 2, Yifan Sun 1, 3, Lenka Zdeborová 4

#### Journal of Statistical Mechanics: Theory and Experiment (2012) P08009

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement protocols in a wide range of applications. Using an interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a strategy that allows compressed sensing to be performed at acquisition rates approaching to the theoretical optimal limits. In this paper, we give a more thorough presentation of our approach, and introduce many new results. We present the probabilistic approach to reconstruction and discuss its optimality and robustness. We detail the derivation of the message passing algorithm for reconstruction and expectation max- imization learning of signal-model parameters. We further develop the asymptotic analysis of the corresponding phase diagrams with and without measurement noise, for different distribution of signals, and discuss the best possible reconstruction performances regardless of the algorithm. We also present new efficient seeding matrices, test them on synthetic data and analyze their performance asymptotically.

• 1. Laboratoire de Physico-Chimie Théorique (LPCT),
CNRS : UMR7083 – ESPCI ParisTech
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. LMIB and School of Mathematics and Systems Science,
Beihang University
• 4. Institut de Physique Théorique (ex SPhT) (IPHT),
CNRS : URA2306 – CEA : DSM/IPHT

Citations to the Article (5)

• ## Probing Spin-Charge Relation by Magnetoconductance in One-Dimensional Polymer Nanofibers

### A. Choi 1, 2, K. H. Kim 1, S. J. Hong 1, M. Goh 3, 4, K. Akagi 3, R. B. Kaner 5, N. N. Kirova 6, S. A. Brazovskii 7, A. T. Johnson 8, 9, D. A. Bonnell 8, E. J. Mele 9, Y. W. Park 1

#### Physical Review B (Condensed Matter) 86 (2012) 155423

Polymer nanofibers are one-dimensional organic hydrocarbon systems containing conducting polymers where the non-linear local excitations such as solitons, polarons and bipolarons formed by the electron-phonon interaction were predicted. Magnetoconductance (MC) can simultaneously probe both the spin and charge of these mobile species and identify the effects of electron-electron interactions on these nonlinear excitations. Here we report our observations of a qualitatively different MC in polyacetylene (PA) and in polyaniline (PANI) and polythiophene (PT) nanofibers. In PA the MC is essentially zero, but it is present in PANI and PT. The universal scaling behavior and the zero (finite) MC in PA (PANI and PT) nanofibers provide evidence of Coulomb interactions between spinless charged solitons (interacting polarons which carry both spin and charge).

• 1. Department of Physics and Astronomy,
Seoul National University
• 2. WCU Flexible Nanosystems,
Korea University
• 3. Department of Polymer Chemistry,
Kyoto University
• 4. Institute of Advanced Composite Materials,
KIST
• 5. Department of Chemistry and Biochemistry,
UCLA
• 6. Laboratoire de Physique des Solides (LPS),
CNRS : UMR8502 – Université Paris XI - Paris Sud
• 7. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 8. Nano-Bio Interface Center,
University of Pennsylvania
• 9. Department of Physics and Astronomy,
University of Pennsylvania

• ## Quantitative field theory of the glass transition

### Silvio Franz, Hugo Jacquin, Giorgio Parisi, Pierfrancesco Urbani, Francesco Zamponi

#### Proceeding of the national academy of sciences 109 (2012) 18725

We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we study analytically the critical behavior of a set of four-points correlation functions from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find results that are consistent with numerical simulations.

• ## Quantum fluctuations around black hole horizons in Bose-Einstein condensates

### P. -É. Larré 1, A. Recati 2, I. Carusotto 2, N. Pavloff 1

#### Physical Review A 85 (2012) 013621

We study several realistic configurations allowing to realize an acoustic horizon in the flow of a one dimensional Bose-Einstein condensate. In each case we give an analytical description of the flow pattern, of the spectrum of Hawking radiation and of the associated quantum fluctuations. Our calculations confirm that the non local correlations of the density fluctuations previously studied in a simplified model provide a clear signature of Hawking radiation also in realistic configurations. In addition we explain by direct computation how this non local signal relates to short range modifications of the density correlations.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. INO-CNR BEC Center and Dipartimento di Fisica,
Universita di Trento

Citations to the Article (9)

• ## Quantum flutter of supersonic particles in one-dimensional quantum liquids

### Charles J. M. Mathy 1, Mikhail B. Zvonarev 1, 2, Eugene Demler 1

#### Nature Physics 8 (2012) 881-886

The non-equilibrium dynamics of strongly correlated many-body systems exhibits some of the most puzzling phenomena and challenging problems in condensed matter physics. Here we report on essentially exact results on the time evolution of an impurity injected at a finite velocity into a one-dimensional quantum liquid. We provide the first quantitative study of the formation of the correlation hole around a particle in a strongly coupled many-body quantum system, and find that the resulting correlated state does not come to a complete stop but reaches a steady state which propagates at a finite velocity. We also uncover a novel physical phenomenon when the impurity is injected at supersonic velocities: the correlation hole undergoes long-lived coherent oscillations around the impurity, an effect we call quantum flutter. We provide a detailed understanding and an intuitive physical picture of these intriguing discoveries, and propose an experimental setup where this physics can be realized and probed directly.

• 1. Department of Physics,
University of Harvard
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Raman scattering of atoms from a quasi-condensate in a perturbative regime

### T. Wasak 1, J. Chwedenczuk 1, M. Trippenbach 1, 2, Pawel Zin 2, 3

#### Physical Review A 86 (2012) 043621

It is demonstrated that measurements of positions of atoms scattered from a quasi-condensate in a Raman process provide information on the temperature of the parent cloud. In particular, the widths of the density and second order correlation functions are sensitive to the phase fluctuations induced by non-zero temperature of the quasi-condensate. It is also shown how these widths evolve during expansion of the cloud of scattered atoms. These results are useful for planning future Raman scattering experiments and indicate the degree of spatial resolution of atom-position measurements necessary to detect the temperature dependence of the quasi-condensate.

• 1. Institute of Theoretical Physics,
Warsaw University
• 2. Andrzej Soltan Institute for Nuclear Studies,
Warsaw University
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Random, blocky and alternating ordering in supramolecular polymers of chemically bidisperse monomers

### Sara Jabbari-Farouji 1, 2, 3, Paul Van Der Schoot 2, 4

#### Journal of Chemical Physics 137 (2012) 064906

As a first step to understanding the role of molecular or chemical polydispersity in self-assembly, we put forward a coarse-grained model that describes the spontaneous formation of quasi-linear polymers in solutions containing two self-assembling species. Our theoretical framework is based on a two-component self-assembled Ising model in which the bidispersity is parameterized in terms of the strengths of the binding free energies that depend on the monomer species involved in the pairing interaction. Depending upon the relative values of the binding free energies involved, different morphologies of assemblies that include both components are formed, exhibiting paramagnetic-, ferromagnetic- or anti ferromagnetic-like order, i.e., random, blocky or alternating ordering of the two components in the assemblies. Analyzing the model for the case of ferromagnetic ordering, which is of most practical interest, we find that the transition from conditions of minimal assembly to those characterized by strong polymerization can be described by a critical concentration that depends on the concentration ratio of the two species. Interestingly, the distribution of monomers in the assemblies is different from that in the original distribution, i.e., the ratio of the concentrations of the two components put into the system. The monomers with a smaller binding free energy are more abundant in short assemblies and monomers with a larger binding affinity are more abundant in longer assemblies. Under certain conditions the two components congregate into separate supramolecular polymeric species and in that sense phase separate. We find strong deviations from the expected growth law for supramolecular polymers even for modest amounts of a second component, provided it is chemically sufficiently distinct from the main one.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Theory of Polymer and Soft Matter Group,
Eindhoven University of Technology
• 3. Dutch Polymer Institute,
Dutch Polymer Institute
• 4. Institute for Theoretical Physics,,
Utrecht University

• ## Reconstruction of financial network for robust estimation of systemic risk

### Iacopo Mastromatteo 1, Elia Zarinelli 2, Matteo Marsili 3

#### Journal of Statistical Mechanics: Theory and Experiment (2012) P03011

In this paper we estimate the propagation of liquidity shocks through interbank markets when the information about the underlying credit network is incomplete. We show that techniques such as Maximum Entropy currently used to reconstruct credit networks severely underestimate the risk of contagion by assuming a trivial (fully connected) topology, a type of network structure which can be very different from the one empirically observed. We propose an efficient message-passing algorithm to explore the space of possible network structures, and show that a correct estimation of the network degree of connectedness leads to more reliable estimations for systemic risk. Such algorithm is also able to produce maximally fragile structures, providing a practical upper bound for the risk of contagion when the actual network structure is unknown. We test our algorithm on ensembles of synthetic data encoding some features of real financial networks (sparsity and heterogeneity), finding that more accurate estimations of risk can be achieved. Finally we find that this algorithm can be used to control the amount of information regulators need to require from banks in order to sufficiently constrain the reconstruction of financial networks.

• 1. Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (SISSA / ISAS),
Scuola Internazionale Superiore di Studi Avanzati/International School for Advanced Studies (SISSA/ISAS)
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. The Abdus Salam International Centre for Theoretical Physics,
ICTP Trieste

• ## Record statistics and persistence for a random walk with a drift

### Satya N. Majumdar 1, Gregory Schehr 1, Gregor Wergen 2

#### Journal of Physics A General Physics 45 (2012) 355002

We study the statistics of records of a one-dimensional random walk of n steps, starting from the origin, and in presence of a constant bias c. At each time-step the walker makes a random jump of length \eta drawn from a continuous distribution f(\eta) which is symmetric around a constant drift c. We focus in particular on the case were f(\eta) is a symmetric stable law with a Lévy index 0 < \mu \leq 2. The record statistics depends crucially on the persistence probability which, as we show here, exhibits different behaviors depending on the sign of c and the value of the parameter \mu. Hence, in the limit of a large number of steps n, the record statistics is sensitive to these parameters (c and \mu) of the jump distribution. We compute the asymptotic mean record number after n steps as well as its full distribution P(R,n). We also compute the statistics of the ages of the longest and the shortest lasting record. Our exact computations show the existence of five distinct regions in the (c, 0 < \mu \leq 2) strip where these quantities display qualitatively different behaviors. We also present numerical simulation results that verify our analytical predictions.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut für Theoretische Physik,
Universität zu Köln

Citations to the Article (8)

• ## Record Statistics for Multiple Random Walks

### Gregor Wergen 1, Satya N. Majumdar 2, Gregory Schehr 2

#### Physical Review E 86 (2012) 011119

We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance \sigma^2 of the jump distribution is finite and (II) when \sigma^2 is divergent as in the case of Lévy flights with index 0 < \mu < 2. In both cases we find that the mean record number grows universally as \sim \alpha_N \sqrt{n} for large n, but with a very different behavior of the amplitude \alpha_N for N > 1 in the two cases. We find that for large N, \alpha_N \approx 2 \sqrt{\log N} independently of \sigma^2 in case I. In contrast, in case II, the amplitude approaches to an N-independent constant for large N, \alpha_N \approx 4/\sqrt{\pi}, independently of 0<\mu<2. For finite \sigma^2 we argue, and this is confirmed by our numerical simulations, that the full distribution of (R_{n,N}/\sqrt{n} - 2 \sqrt{\log N}) \sqrt{\log N} converges to a Gumbel law as n \to \infty and N \to \infty. In case II, our numerical simulations indicate that the distribution of R_{n,N}/\sqrt{n} converges, for n \to \infty and N \to \infty, to a universal nontrivial distribution, independently of \mu. We discuss the applications of our results to the study of the record statistics of 366 daily stock prices from the Standard & Poors 500 index.

• 1. Institut für Theoretische Physik,
Universität zu Köln
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (4)

• ## Self-assembly of spherical interpolyelectrolyte complexes from oppositely charged polymers

### Vladimir A. Baulin 1, 2, Emmanuel Trizac 3

#### Soft Matter 8 (2012) 2755-2766

The formation of inter-polyelectrolyte complexes from the association of oppositely charged polymers in an electrolyte is studied. The charged polymers are linear oppositely charged polyelectrolytes, with possibly a neutral block. This leads to complexes with a charged core, and a more dilute corona of dangling chains, or of loops (flower-like structure). The equilibrium aggregation number of the complexes (number of polycations m+ and polyanions m-) is determined by minimizing the relevant free energy functional, the Coulombic contribution of which is worked out within Poisson-Boltzmann theory. The complexes can be viewed as colloids that are permeable to micro-ionic species, including salt. We find that the complexation process can be highly specific, giving rise to very localized size distribution in composition space (m+,m-).

• 1. Institució Catalana de Recerca i Estudis Avançats [Barcelona] (ICREA),
ICREA – Universitat de Barcelona – Fundació Catalana per a la Recerca i la Innovació (FCRI)
• 2. Departament d'Enginyeria Quimica,
Universitat Rovira i Virgili
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Short time growth of a KPZ interface with flat initial conditions

### Thomas Gueudre 1, Pierre Le Doussal 1, Alberto Rosso 2, Adrien Henry 2, Pasquale Calabrese 3

#### Physical Review E 86 (2012) 041151

The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other fixed. From these expressions, the short time expansions of the lowest cumulants of the KPZ height field are exactly derived. The results for these two classes of cumulants are checked in high precision lattice numerical simulations. The short time limit considered here is relevant for the study of the interface growth in the large diffusivity/weak noise limit, and describes the universal crossover between the Edwards-Wilkinson and KPZ universality classes for an initially flat interface.

• 1. Laboratoire de Physique Théorique de l'ENS (LPTENS),
CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Dipartimento di Fisica dell'Universita di Pisa and INFN,Pisa,
UNIVERSITÀ DEGLI STUDI DI PISA

Citations to the Article (2)

• ## Slow quench dynamics of Mott-insulating regions in a trapped Bose gas

### Jean-Sebastien Bernier 1, 2, Dario Poletti 3, Peter Barmettler 3, Guillaume Roux 4, Corinna Kollath 1, 5

#### Physical Review A 85 (2012) 033641

We investigate the dynamics of Mott-insulating regions of a trapped bosonic gas as the interaction strength is changed linearly with time. The bosonic gas considered is loaded into an optical lattice and confined to a parabolic trapping potential. Two situations are addressed: the formation of Mott domains in a superfluid gas as the interaction is increased, and their melting as the interaction strength is lowered. In the first case, depending on the local filling, Mott-insulating barriers can develop and hinder the density and energy transport throughout the system. In the second case, the density and local energy adjust rapidly whereas long range correlations require longer time to settle. For both cases, we consider the time evolution of various observables: the local density and energy, and their respective currents, the local compressibility, the local excess energy, the heat and single particle correlators. The evolution of these observables is obtained using the time-dependent density-matrix renormalization group technique and comparisons with time-evolutions done within the Gutzwiller approximation are provided.

• 1. Centre de Physique Théorique (CPHT),
CNRS : UMR7644 – Polytechnique - X
• 2. Department of Physics and Astronomy,
University of British Columbia
• 3. Département de Physique Théorique,
Université de Genève
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 5. Département de physique théorique,
Université de Genève

Citations to the Article (6)

• ## Spectral determinants and zeta functions of Schrödinger operators on metric graphs

### J. M. Harrison 1, K. Kirsten 1, C. Texier 2, 3

#### Journal of Physics A: Mathematical and Theoretical 45 (2012) 125206

A derivation of the spectral determinant of the Schrödinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form classified according to the scheme of Kostrykin and Schrader. To formulate the spectral determinant we first derive the spectral zeta function of the Schrödinger operator using an appropriate secular equation. The result obtained for the spectral determinant is along the lines of the recent conjecture.

• 1. Department of Mathematics,
Baylor University
• 2. Laboratoire de Physique des Solides (LPS),
CNRS : UMR8502 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Statistical physics-based reconstruction in compressed sensing

### Florent Krzakala 1, Marc Mézard 2, François Sausset 2, Yifan Sun 1, 3, Lenka Zdeborová 4

#### Physical Review X 2 (2012) 021005

Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is measured. Currently used reconstruction techniques are, however, limited to acquisition rates larger than the true density of the signal. We design a new procedure which is able to reconstruct exactly the signal with a number of measurements that approaches the theoretical limit in the limit of large systems. It is based on the joint use of three essential ingredients: a probabilistic approach to signal reconstruction, a message-passing algorithm adapted from belief propagation, and a careful design of the measurement matrix inspired from the theory of crystal nucleation. The performance of this new algorithm is analyzed by statistical physics methods. The obtained improvement is confirmed by numerical studies of several cases.

• 1. Laboratoire de Physico-Chimie Théorique (LPCT),
CNRS : UMR7083 – ESPCI ParisTech
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. LMIB and School of Mathematics and Systems Science,,
Beihang University
• 4. Institut de Physique Théorique (ex SPhT) (IPHT),
CNRS : URA2306 – CEA : DSM/IPHT

Citations to the Article (16)

• ## Strong-coupling theory for a polarizable planar colloid

### L. Samaj 1, 2, E. Trizac 2

#### Contributions to Plasma Physics 52 (2012) 53

We propose a strong-coupling analysis of a polarizable planar interface, in the spirit of a recently introduced Wigner-Crystal formulation. The system is made up of two moieties: a semi-infinite medium (z<0) with permittivity epsilon' while the other half space in z>0 is occupied by a solution with permittivity epsilon, and mobile counter-ions (no added electrolyte). The interface at z=0 bears a uniform surface charge. The counter-ion density profile is worked out explicitly for both repulsive and attractive dielectric image cases.

• 1. Institute of Physics,
Slovak Academy of Sciences
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Structure factors in granular experiments with homogeneous fluidization

### A. Puglisi 1, A. Gnoli 2, 3, G. Gradenigo 4, A. Sarracino 5, D. Villamaina 6

Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2d fluidized granular experiment, with packing fractions $\phi\in[10%,40%]$. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the 'bath' temperature $T_b$, depending on shaking parameters, and the 'granular' temperature $T_g • 1. Dipartimento di Fisica, Università La Sapienza • 2. Dipartimento di Fisica, Università degli studi di Roma "La Sapienza" • 3. Istituto dei Sistemi Complessi, CNR - Consiglio Nationale delle Ricerche • 4. Dipartimento di Fisica, CNR - Consiglio Nationale delle Ricerche • 5. Dipartimento di Fisica, CNR - Consiglio Nationale delle Ricerche • 6. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud Download PDF via arXiV.org • ## Structure of trajectories of complex matrix eigenvalues in the Hermitian-non-Hermitian transition ### O. Bohigas 1, J. X. de Carvalho 2, 3, M. P. Pato 2 #### Physical Review E 86 (2012) 031118 The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane. • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud • 2. Instituto de Fisica, Universidade de São Paulo • 3. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut Download PDF via arXiV.org • ## Super-Rough Glassy Phase of the Random Field XY Model in Two Dimensions ### Anthony Perret 1, Zoran Ristivojevic 2, Pierre Le Doussal 2, Gregory Schehr 1, Kay J. Wiese 2 #### Physical Review Letters 109 (2012) 157205 We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the critical temperature$T_c$, the disorder and thermally averaged correlation function$B(r)$of the phase field$\theta(x)$,$B(r) = \bar{<[\theta(x) - \theta(x+ r) ]^2>}$behaves, for$r \gg a$, as$B(r) \simeq A(\tau) \ln^2 (r/a)$where$r = |r|$and$a$is a microscopic length scale. We derive the RG equations up to cubic order in$\tau = (T_c-T)/T_c$and predict the universal amplitude${A}(\tau) = 2\tau^2-2\tau^3 + {\cal O}(\tau^4)$. The universality of$A(\tau)$results from nontrivial cancellations between nonuniversal constants of RG equations. Using an exact polynomial algorithm on an equivalent dimer version of the model we compute${A}(\tau)$numerically and obtain a remarkable agreement with our analytical prediction, up to$\tau \approx 0.5$. • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud • 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris Download PDF via arXiV.org Citations to the Article (1) • ## Survival probability of an immobile target surrounded by mobile traps ### Jasper Franke 1, Satya N. Majumdar 2 #### Journal of Statistical Mechanics: Theory and Experiment (2012) P05024 We study analytically, in one dimension, the survival probability$P_{s}(t)$up to time$t$of an immobile target surrounded by mutually noninteracting traps each performing a continuous-time random walk (CTRW) in continuous space. We consider a general CTRW with symmetric and continuous (but otherwise arbitrary) jump length distribution$f(\eta)$and arbitrary waiting time distribution$\psi(\tau)$. The traps are initially distributed uniformly in space with density$\rho$. We prove an exact relation, valid for all time$t$, between$P_s(t)$and the expected maximum$E[M(t)]$of the trap process up to time$t$, for rather general stochastic motion$x_{\rm trap}(t)$of each trap. When$x_{\rm trap}(t)$represents a general CTRW with arbitrary$f(\eta)$and$\psi(\tau)$, we are able to compute exactly the first two leading terms in the asymptotic behavior of$E[M(t)]$for large$t$. This allows us subsequently to compute the precise asymptotic behavior,$P_s(t)\sim a\, \exp[-b\, t^{\theta}]$, for large$t$, with exact expressions for the stretching exponent$\theta$and the constants$a$and$b$for arbitrary CTRW. By choosing appropriate$f(\eta)$and$\psi(\tau)\$, we recover the previously known results for diffusive and subdiffusive traps. However, our result is more general and includes, in particular, the superdiffusive traps as well as totally anomalous traps.

• 1. Institut für Theoretische Physik,
Universität zu Köln
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (2)

• ## The game of go as a complex network

### Bertrand Georgeot 1, Olivier Giraud 2

#### Europhysics Letters 97, 6 (2012) 68002

We study the game of go from a complex network perspective. We construct a directed network using a suitable definition of tactical moves including local patterns, and study this network for different datasets of professional tournaments and amateur games. The move distribution follows Zipf's law and the network is scale free, with statistical peculiarities different from other real directed networks, such as e. g. the World Wide Web. These specificities reflect in the outcome of ranking algorithms applied to it. The fine study of the eigenvalues and eigenvectors of matrices used by the ranking algorithms singles out certain strategic situations. Our results should pave the way to a better modelization of board games and other types of human strategic scheming.

• 1. Laboratoire de Physique Théorique - IRSAMC (LPT),
CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Trace formula for dielectric cavities III: TE modes

### E. Bogomolny 1, R. Dubertrand 2

#### Physical Review E 86 (2012) 026202

The construction of the semiclassical trace formula for the resonances with the transverse electric (TE) polarization for two-dimensional dielectric cavities is discussed. Special attention is given to the derivation of the two first terms of Weyl's series for the average number of such resonances. The obtained formulas agree well with numerical calculations for dielectric cavities of different shapes.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut fur Theoretische Physik,
University of Heidelberg

• ## Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects

### Matthias Krüger 1, Giuseppe Bimonte 2, Thorsten Emig 3, Mehran Kardar 1

#### Physical Review B 86 (2012) 115423

We present a detailed derivation of heat radiation, heat transfer and (Casimir) interactions for N arbitrary objects in the framework of fluctuational electrodynamics in thermal non-equilibrium. The results can be expressed as basis-independent trace formulae in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave-expansions, we transform the results for radiation, transfer and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nano-spheres is typically invalid. We derive asymptotic formulae for heat transfer and non-equilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nano-sphere can levitate above a plate with the repulsive non-equilibrium force overcoming gravity -- an effect that is not due to radiation pressure.

• 1. Department of Physics,
Massachusetts Institute of Technology
• 2. Dipartimento di Scienze Fisiche,
Universita di Napoli Federico II
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Tuning spreading and avalanche-size exponents in directed percolation with modified activation probabilities

### François Landes 1, E. A. Jagla 2, Alberto Rosso 1

#### Physical Review E 86 (2012) 041150

We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value p_c. Criticality is lost as soon as the probability to activate sites at the first attempt, p1, is changed. We show here that criticality can be restored by 'compensating' the change in p1 by an appropriate change of the second time activation probability p2 in the opposite direction. At compensation, we observe that the bulk exponents of the process coincide with those of the normal directed percolation process. However, the spreading exponents are changed, and take values that depend continuously on the pair (p1, p2). We interpret this situation by acknowledging that the model with modified initial probabilities has an infinite number of absorbing states.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Centro Atómico Bariloche and Instituto Balseiro,
Comision Nacional de Energia Atomica

• ## Universal reference state in a driven homogeneous granular gas

### M. I. Garcia de Soria 1, P. Maynar 1, E. Trizac 2

#### Physical Review E 85 (2012) 051301

We study the dynamics of a homogeneous granular gas heated by a stochastic thermostat, in the low density limit. It is found that, before reaching the stationary regime, the system quickly 'forgets' the initial condition and then evolves through a universal state that does not only depend on the dimensionless velocity, but also on the instantaneous temperature, suitably renormalized by its steady state value. We find excellent agreement between the theoretical predictions at Boltzmann equation level for the one-particle distribution function, and Direct Monte Carlo simulations. We conclude that at variance with the homogeneous cooling phenomenology, the velocity statistics should not be envisioned as a single-parameter, but as a two-parameter scaling form, keeping track of the distance to stationarity.

• 1. Fisica Teorica, Universidad de Sevilla,
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

Citations to the Article (3)

• ## Wave pattern induced by a localized obstacle in the flow of a one-dimensional polariton condensate

### P. -É Larré 1, N. Pavloff 1, A. M. Kamchatnov 2

#### Physical Review B 86 (2012) 165304

Motivated by recent experiments on generation of wave patterns by a polariton condensate incident on a localized obstacle, we study the characteristics of such flows under the condition that irreversible processes play a crucial role in the system. The dynamics of a non-resonantly pumped polariton condensate in a quasi-one-dimensional quantum wire is modeled by a Gross-Pitaevskii equation with additional phenomenological terms accounting for the dissipation and pumping processes. The response of the condensate flow to an external potential describing a localized obstacle is considered in the weak-perturbation limit and also in the nonlinear regime. The transition from a viscous drag to a regime of wave resistance is identified and studied in detail.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institute of Spectroscopy,
Russian Academy of Sciences

• ## Wavepacket Dynamics in Nonlinear Schrödinger Equations

### Simon Moulieras 1, Alejandro G. Monastra 2, 3, Marcos Saraceno 4, Patricio Leboeuf 1

#### Physical Review A 85 (2012) 013841

Coherent states play an important role in quantum mechanics because of their unique properties under time evolution. Here we explore this concept for one-dimensional repulsive nonlinear Schrödinger equations, which describe weakly interacting Bose-Einstein condensates or light propagation in a nonlinear medium. It is shown that the dynamics of phase-space translations of the ground state of a harmonic potential is quite simple: the centre follows a classical trajectory whereas its shape does not vary in time. The parabolic potential is the only one that satis?fies this property. We study the time evolution of these nonlinear coherent states under perturbations of their shape, or of the confi?ning potential. A rich variety of e?ects emerges. In particular, in the presence of anharmonicities, we observe that the packet splits into two distinct components. A fraction of the condensate is transferred towards uncoherent high-energy modes, while the amplitude of oscillation of the remaining coherent component is damped towards the bottom of the well.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Gerencia Investigación y Aplicaciones,
Comision Nacional de Energia Atomica
• 3. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET),
University of Buenos Aires
• 4. Gerencia Investigación y Aplicaciones,
Comision Nacional de Energia Atomica

Citations to the Article (2)

• ## Archive ouverte HAL – Mesoscopic Anderson Box: Connecting Weak to Strong Coupling

### Dong E. Liu 1, * Sébastien Burdin 2 Harold U. Baranger 1 Denis Ullmo 3

#### Physical Review B : Condensed matter and materials physics, American Physical Society, 2012, 85 (15), pp.155455 (1-17). 〈10.1103/PhysRevB.85.155455〉

Both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. In an Anderson box, mesoscopic fluctuations of the effective single particle properties will be large. We study how the statistical fluctuations at low temperature in these two problems are connected, using random matrix theory and the slave boson mean field approximation (SBMFA). First, for a resonant level model such as results from the SBMFA, we find the joint distribution of energy levels with and without the resonant level present. Second, if only energy levels within the Kondo resonance are considered, the distributions of perturbed levels collapse to universal forms for both orthogonal and unitary ensembles for all values of the coupling. These universal curves are described well by a simple Wigner-surmise type toy model. Third, we study the fluctuations of the mean field parameters in the SBMFA, finding that they are small. Finally, the change in the intensity of an eigenfunction at an arbitrary point is studied, such as is relevant in conductance measurements: we find that the introduction of the strongly-coupled impurity considerably changes the wave function but that a substantial correlation remains.

• 1. Duke Physics
• 2. LOMA - Laboratoire Ondes et Matière d'Aquitaine
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

• ## Membrane shape at the edge of the dynamin helix sets location and duration of the fission reaction.

### Sandrine Morlot 1, 2 Valentina Galli 1 Marius Klein 2 Nicolas Chiaruttini 3 John Manzi 2 Frédéric Humbert 1 Luis DinisMartin Lenz 4 Giovanni Cappello 2 Aurélien Roux 1

#### Cell, Elsevier (Cell Press), 2012, 151 (3), pp.619-29

The GTPase dynamin polymerizes into a helical coat that constricts membrane necks of endocytic pits to promote their fission. However, the dynamin mechanism is still debated because constriction is necessary but not sufficient for fission. Here, we show that fission occurs at the interface between the dynamin coat and the uncoated membrane. At this location, the considerable change in membrane curvature increases the local membrane elastic energy, reducing the energy barrier for fission. Fission kinetics depends on tension, bending rigidity, and the dynamin constriction torque. Indeed, we experimentally find that the fission rate depends on membrane tension in vitro and during endocytosis in vivo. By estimating the energy barrier from the increased elastic energy at the edge of dynamin and measuring the dynamin torque, we show that the mechanical energy spent on dynamin constriction can reduce the energy barrier for fission sufficiently to promote spontaneous fission. :

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

• ## Charge-density waves studied at the surface and at the atomic scale in NbSe3

### Pierre Monceau 1 C. Brun 2 Zhao-Zhong Wang 2 S. Brazovskii 3

#### Physica B: Condensed Matter, Elsevier, 2012, 407 (11), pp.1845

We have studied by scanning tunneling microscopy (STM) the two charge-density wave (CDW) transitions in NbSe3 on in situ cleaved (b,c) plane. We could identify the three types of chains existing inside a single unit cell as well as characterize how both CDWs are distributed on these elementary chains. We also followed between 5 and 140 K the temperature dependence of first-order CDW satellite spots, obtained from the Fourier transform of the STM images, to extract the surface critical temperatures (T-s). Whereas the high-temperature CDW appears to have comparable critical temperature to the bulk one, the low-T CDW transition occurs at T-2s = 70-75 K, more than 15 K above the bulk T-2b = 59 K while at exactly the same wave number. A reasonable mechanism for such an unusually high surface enhancement is a softening of transverse phonon modes involved in the CDW formation.

• 1. CristElec MagSup
• 2. LPN - Laboratoire de photonique et de nanostructures
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• ## Archive ouverte HAL – From Weak- to Strong-Coupling Mesoscopic Fermi Liquids

### Dong E. Liu 1 Sébastien Burdin 2 Harold U. Baranger 1 Denis Ullmo 3

#### EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2012, 97 (1), pp.17006. 〈10.1209/0295-5075/97/17006〉

We study mesoscopic fluctuations in a system in which there is a continuous connection between two distinct Fermi liquids, asking whether the mesoscopic variation in the two limits is correlated. The particular system studied is an Anderson impurity coupled to a finite mesoscopic reservoir described by random matrix theory, a structure which can be realized using quantum dots. We use the slave boson mean field approach to connect the levels of the uncoupled system to those of the strong coupling Noziéres Fermi liquid. We find strong but not complete correlation between the mesoscopic properties in the two limits and several universal features.

• 1. Duke Physics
• 2. LOMA - Laboratoire Ondes et Matière d'Aquitaine
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

• ## Finite-temperature and finite-time scaling of the directed polymer free-energy with respect to its geometrical fluctuations

### Elisabeth Agoritsas 1, * Sebastian Bustingorry 2 Vivien Lecomte 3 Gregory Schehr 4 Thierry Giamarchi 1

#### Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2012, 86 (3), pp.031144. <10.1103/PhysRevE.86.031144>

We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse fluctuations of the directed polymer, described by its roughness, and the fluctuations of its free-energy, characterized by its two-point correlator. Analytical arguments are provided in favor of a generic scaling law between those quantities, at finite time, non-vanishing {\xi} and explicit temperature dependence. Numerical results are in good agreement both for simulations on the discrete directed polymer and on a continuous directed polymer (with short-range correlated disorder). Applications to recent experiments on liquid crystals are discussed.

• 1. DPMC - Département de Physique de la Matière Condensée
• 2. Centro Atomico Bariloche
• 3. LPMA - Laboratoire de Probabilités et Modèles Aléatoires
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

We report on scanning-tunneling microscopy experiments in a charge-density wave (CDW) system allowing visually capturing and studying in detail the individual solitons corresponding to the self-trapping of just one electron. This Amplitude Soliton'' is marked by vanishing of the CDW amplitude and by the pi shift of its phase. It might be the realization of the spinon-the long-sought particle (along with the holon) in the study of science of strongly correlated electronic systems. As a distinct feature we also observe one-dimensional Friedel oscillations superimposed on the CDW which develop independently of solitons.