# LPTMS Publications

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## A simple derivation of the Tracy-Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix

### Celine Nadal

^{1}, Satya N. Majumdar^{1}#### Journal of statistical mechanics-theory and experiment (2011) P04001

In this paper, we first briefly review some recent results on the distribution of the maximal eigenvalue of a $(N\times N)$ random matrix drawn from Gaussian ensembles. Next we focus on the Gaussian Unitary Ensemble (GUE) and by suitably adapting a method of orthogonal polynomials developed by Gross and Matytsin in the context of Yang-Mills theory in two dimensions, we provide a rather simple derivation of the Tracy-Widom law for GUE. Our derivation is based on the elementary asymptotic scaling analysis of a pair of coupled nonlinear recursion relations. As an added bonus, this method also allows us to compute the precise subleading terms describing the right large deviation tail of the maximal eigenvalue distribution. In the Yang-Mills language, these subleading terms correspond to non-perturbative (in $1/N$ expansion) corrections to the two-dimensional partition function in the so called 'weak' coupling regime.

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

**4**)## Adversarial Satisfiability Problem

### Michele Castellana

^{1, 2}, Lenka Zdeborová^{3}#### Journal of statistical mechanics-theory and experiment (2011) P03023

We study the adversarial satisfiability problem, where the adversary can choose whether variables are negated in clauses or not in order to make the resulting formula unsatisfiable. This is one case of a general class of adversarial optimization problems that often arise in practice and are algorithmically much harder than the standard optimization problems. We use the cavity method to compute large deviations of the entropy in the random satisfiability problem with respect to the negation-configurations. We conclude that in the thermodynamic limit the best strategy the adversary can adopt is extremely close to simply balancing the number of times every variable is and is not negated. We also conduct a numerical study of the problem, and find that there are very strong pre-asymptotic effects that are due to the fact that for small sizes exponential and factorial growth is hardly distinguishable.

- 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 2. Dipartimento di Fisica and INFM, Università degli studi di Roma I - La Sapienza
- 3. Institut de Physique Théorique (ex SPhT) (IPHT), CNRS : URA2306 – CEA : DSM/IPHT

## Algebraic and arithmetic area for $m$ planar Brownian paths

### Jean Desbois

^{1}, Stephane Ouvry^{1}#### Journal of statistical mechanics-theory and experiment (2011) P05024

The leading and next to leading terms of the average arithmetic area $< S(m)>$ enclosed by $m\to\infty$ independent closed Brownian planar paths, with a given length $t$ and starting from and ending at the same point, is calculated. The leading term is found to be $< S(m) > \sim {\pi t\over 2}\ln m$ and the $0$-winding sector arithmetic area inside the $m$ paths is subleading in the asymptotic regime. A closed form expression for the algebraic area distribution is also obtained and discussed.

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

## Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications

### Aurelien Decelle

^{1}, Florent Krzakala^{2}, Cristopher Moore^{3, 4}, Lenka Zdeborová^{5}#### Physical Review E

**84**(2011) 066106In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We describe in detail properties of the detectability/undetectability phase transition and the easy/hard phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.

- 2. Laboratoire de Physico-Chimie Théorique (LPCT), CNRS : UMR7083 – ESPCI ParisTech
- 3. Department of Computer Science - UNM, University of New Mexico
- 4. Sante Fe Institute (SFI), -
- 5. Institut de Physique Théorique (ex SPhT) (IPHT), CNRS : URA2306 – CEA : DSM/IPHT

**6**)## Atom-dimer and dimer-dimer scattering in fermionic mixtures near a narrow Feshbach resonance

### J. Levinsen

^{1, 2}, D. S. Petrov^{1, 3}#### European Physical Journal D

**65**(2011) 67-82We develop a diagrammatic approach for solving few-body problems in heteronuclear fermionic mixtures near a narrow interspecies Feshbach resonance. We calculate s-, p-, and d-wave phaseshifts for the scattering of an atom by a weakly-bound dimer. The fermionic statistics of atoms and the composite nature of the dimer lead to a strong angular momentum dependence of the atom-dimer interaction, which manifests itself in a peculiar interference of the scattered s- and p-waves. This effect strengthens with the mass ratio and is remarkably pronounced in 40K-(40K-6Li) atom-dimer collisions. We calculate the scattering length for two dimers formed near a narrow interspecies resonance. Finally, we discuss the collisional relaxation of the dimers to deeply bound states and evaluate the corresponding rate constant as a function of the detuning and collision energy.

- 2. TCM Group, Cavendish Laboratory, Cavendish Laboratory Cambridge
- 3. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow

**10**)## Casimir force between sharp-shaped conductors

### Mohammad F. Maghrebi

^{1}, Sahand Jamal Rahi^{1, 2}, Thorsten Emig^{3}, Noah Graham^{4}, Robert L. Jaffe^{1}, Mehran Kardar^{1}#### Proceeding of the national academy of sciences

**108**(2011) 6867-6871Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest.

- 1. Department of Physics, Massachusetts Institute of Technology
- 2. Center for Studies in Physics and Biology, The Rockefeller University
- 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 4. Middlebury College, Middlebury Colleg

**16**)## Characterizing order in amorphous systems

### François Sausset

^{1, 2}, Dov Levine^{1}#### Physical Review Letters

**107**(2011) 045501We measure and compare three correlation lengths proposed to describe the extent of structural order in amorphous systems. In particular, the recently proposed 'patch correlation length' is measured as a function of temperature and fragility and shown to be comparable with other measures. In addition, we demonstrate that the patch method also allows us to characterize the symmetries of the local order without any a priori knowledge of it.

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

**12**)## CODA (crossover distribution analyser): quantitative characterization of crossover position patterns along chromosomes

### Gauthier, F., Martin, O.C., Falque, M.

#### BMC Bioinformatics12 (2011) 27

## Colloidal ionic complexes on periodic substrates: ground state configurations and pattern switching

### Samir El Shawish

^{1}, Jure Dobnikar^{1}, Emmanuel Trizac^{2}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**83**(2011) 041403We theoretically and numerically studied ordering of 'colloidal ionic clusters' on periodic substrate potentials as those generated by optical trapping. Each cluster consists of three charged spherical colloids: two negatively and one positively charged. The substrate is a square or rectangular array of traps, each confining one such cluster. By varying the lattice constant from large to small, the observed clusters are first rod-like and form ferro- and antiferro-like phases, then they bend into a banana-like shape and finally condense into a percolated structure. Remarkably, in a broad parameter range between single-cluster and percolated structures, we have found stable supercomplexes composed of six colloids forming grape-like or rocket-like structures. We investigated the possibility of macroscopic pattern switching by applying external electrical fields.

- 1. Jozef Stefan Institute, Jozef Stefan Institute
- 2. LPTMS, University Paris Sud

## Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture

### H. Nonne

^{1}, P. Lecheminant^{1}, Sylvain Capponi^{2}, G. Roux^{3}, E. Boulat^{4}#### Physical Review B

**84**(2011) 125123We investigate the nature of the Mott-insulating phases of half-filled 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of conformal field theory techniques and large-scale DMRG calculations, we show that the phase diagram strongly depends on the parity of $N$. First, we single out charged, spin-singlet, degrees of freedom, that carry a pseudo-spin ${\cal S}=N/2$ allowing to formulate a Haldane conjecture: for attractive interactions, we establish the emergence of Haldane insulating phases when $N$ is even, whereas a metallic behavior is found when $N$ is odd. We point out that the $N=1,2$ cases do \emph{not} have the generic properties of each family. The metallic phase for $N$ odd and larger than 1 has a quasi-long range singlet pairing ordering with an interesting edge-state structure. Moreover, the properties of the Haldane insulating phases with even $N$ further depend on the parity of N/2. In this respect, within the low-energy approach, we argue that the Haldane phases with N/2 even are not topologically protected but equivalent to a topologically trivial insulating phase and thus confirm the recent conjecture put forward by Pollmann {\it et al.} [Pollmann {\it et al.}, arXiv:0909.4059 (2009)].

- 1. Laboratoire de Physique Théorique et Modélisation (LPTM), CNRS : UMR8089 – Université de Cergy Pontoise
- 2. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
- 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 4. Matériaux et Phénomènes Quantiques (MPQ), CNRS : UMR7162 – CNRS : FR2437 – Université Paris VII - Paris Diderot

**4**)## Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model

### Benoit Estienne

^{1, 2}, Vincent Pasquier^{3}, Raoul Santachiara^{4, 5}, Didina Serban^{3}#### Nuclear Physics B

**860**(2011) 377-420We study the properties of the conformal blocks of the conformal field theories with Virasoro or W-extended symmetry. When the conformal blocks contain only second-order degenerate fields, the conformal blocks obey second order differential equations and they can be interpreted as ground-state wave functions of a trigonometric Calogero-Sutherland Hamiltonian with non-trivial braiding properties. A generalized duality property relates the two types of second order degenerate fields. By studying this duality we found that the excited states of the Calogero-Sutherland Hamiltonian are characterized by two partitions, or in the case of WA_{k-1} theories by k partitions. By extending the conformal field theories under consideration by a u(1) field, we find that we can put in correspondence the states in the Hilbert state of the extended CFT with the excited non-polynomial eigenstates of the Calogero-Sutherland Hamiltonian. When the action of the Calogero-Sutherland integrals of motion is translated on the Hilbert space, they become identical to the integrals of motion recently discovered by Alba, Fateev, Litvinov and Tarnopolsky in Liouville theory in the context of the AGT conjecture. Upon bosonisation, these integrals of motion can be expressed as a sum of two, or in general k, bosonic Calogero-Sutherland Hamiltonian coupled by an interaction term with a triangular structure. For special values of the coupling constant, the conformal blocks can be expressed in terms of Jack polynomials with pairing properties, and they give electron wave functions for special Fractional Quantum Hall states

- 1. Institute for Theoretical Physics, Universiteit van Amsterdam
- 2. Department of Physics, Princeton University
- 3. Institut de Physique Théorique (ex SPhT) (IPHT), CNRS : URA2306 – CEA : DSM/IPHT
- 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 5. Laboratoire J.V. Poncelet, UMI 2615

## Counter-ions at Charged Walls: Two Dimensional Systems

### L. Samaj

^{1}, E. Trizac^{2}#### The European Physical Journal Special Topics

**34**(2011) 20We study equilibrium statistical mechanics of classical point counter-ions, formulated on 2D Euclidean space with logarithmic Coulomb interactions (infinite number of particles) or on the cylinder surface (finite particle numbers), in the vicinity of a single uniformly charged line (one single double-layer), or between two such lines (interacting double-layers). The weak-coupling Poisson-Boltzmann theory, which applies when the coupling constant Gamma is small, is briefly recapitulated (the coupling constant is defined as Gamma = beta e^2 where beta is the inverse temperature, and e the counter-ion charge). The opposite strong-coupling limit (Gamma -> infinity) is treated by using a recent method based on an exact expansion around the ground-state Wigner crystal of counter-ions. The weak- and strong-coupling theories are compared at intermediary values of the coupling constant Gamma=2 gamma (gamma=1,2,3), to exact results derived within a 1D lattice representation of 2D Coulomb systems in terms of anti-commuting field variables. The models (density profile, pressure) are solved exactly for any particles numbers N at Gamma=2 and up to relatively large finite N at Gamma=4 and 6. For the one-line geometry, the decay of the density profile at asymptotic distance from the line undergoes a fundamental change with respect to the mean-field behavior at Gamma=6. The like-charge attraction regime, possible in the strong coupling limit but precluded at mean-field level, survives for Gamma=4 and 6, but disappears at Gamma=2.

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

## Critical interfaces and duality in the Ashkin Teller model

### Picco, M., Santachiara, R.

#### Physical Review E83 (2011) 061124

Details## Diffusion with Optimal Resetting

### Martin R. Evans

^{1}, Satya N. Majumdar^{2}#### Journal of Physics A: Mathematical and Theoretical

**44**(2011) 435001We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate $r$. We consider several generalisations of the model of M. R. Evans and S. N. Majumdar (2011), Diffusion with stochastic resetting, Phys. Rev. Lett. 106, 160601: (i) a space dependent resetting rate $r(x)$ ii) resetting to a random position $z$ drawn from a resetting distribution ${\cal P}(z)$ iii) a spatial distribution for the absorbing target $P_T(x)$. As an example of (i) we show that the introduction of a non-resetting window around the initial position can reduce the mean time to absorption provided that the initial position is sufficiently far from the target. We address the problem of optimal resetting, that is, minimising the mean time to absorption for a given target distribution. For an exponentially decaying target distribution centred at the origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows.

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

## Diffusion with Stochastic Resetting

### Martin R. Evans

^{1}, Satya N. Majumdar^{2}#### Physical Review Letters

**106**(2011) 160601We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r^*. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.

- 1. SUPA, School of Physics, University of Edinburgh, SUPA

## Dilution and resonance enhanced repulsion in non-equilibrium fluctuation forces

### Giuseppe Bimonte

^{1}, Thorsten Emig^{2}, Matthias Kruger^{3}, Mehran Kardar^{3}#### Physical Review A

**84**(2011) 042503In equilibrium, forces induced by fluctuations of the electromagnetic field between electrically polarizable objects (microscopic or macroscopic) in vacuum are always attractive. The force may, however, become repulsive for microscopic particles coupled to thermal baths with different temperatures. We demonstrate that this non-equilibrium repulsion can be realized also between macroscopic objects, as planar slabs, if they are kept at different temperatures. It is shown that repulsion can be enhanced by (i) tuning of material resonances in the thermal region, and by (ii) reducing the dielectric contrast due to 'dilution'. This can lead to stable equilibrium positions. We discuss the realization of these effects for aerogels, yielding repulsion down to sub-micron distances at realistic porosities.

- 1. Dipartimento di Scienze Fisiche, Universita di Napoli Federico II
- 3. Department of Physics, Massachusetts Institute of Technology

## Distribution of Parental Genome Blocks in Recombinant Inbred Lines

### Martin, O.C., Hospital, F.

#### Genetics189 (2011) 645-654

## Eigenfunction entropy and spectral compressibility for critical random matrix ensembles

### E. Bogomolny

^{1}, O. Giraud^{1}#### Physical Review Letters

**106**(2011) 044101Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D_1 and the spectral compressibility chi are related by the simple equation chi+D_1/d=1, where d is the system dimensionality.

**12**)## Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries

### Noah Graham

^{1}, Alexander Shpunt^{2}, Thorsten Emig^{3}, Sahand Jamal Rahi^{2, 4}, Robert L. Jaffe^{2}, Mehran Kardar^{2}#### Physical Review D

**83**(2011) 125007An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the 'knife-edge' limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.

- 1. Middlebury College, Middlebury Colleg
- 2. Department of Physics, Massachusetts Institute of Technology
- 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 4. Center for Studies in Physics and Biology, The Rockefeller University

**4**)## Entropy of continuous mixtures and the measure problem

### P. Maynar

^{1}, E. Trizac^{2}#### Physical Review Letters

**106**(2011) 160603In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a 'measure' problem that results from improper weighting of phase space. This issue is addressed considering a generic collision process whereby a large number of particles/agents randomly and repeatedly interact in pairs, with prescribed conservation law(s). We find a sufficient condition under which the stationary single particle distribution function maximizes an entropy-like functional, that is free of the measure problem. This condition amounts to a factorization property of the Jacobian associated to the binary collision law, from which the proper weighting of phase space directly follows.

- 1. Fisica Teorica, Universidad de Sevilla, Universidad de Sevilla

## Environmental versatility promotes modularity in genome-scale metabolic networks

### Areejit Samal

^{1, 2}, Andreas Wagner^{3, 4, 5}, Olivier C. Martin^{2, 6}#### BMC Systems Biology

**5**(2011) 135The ubiquity of modules in biological networks may result from an evolutionary benefit of a modular organization. For instance, modularity may increase the rate of adaptive evolution, because modules can be easily combined into new arrangements that may benefit their carrier. Conversely, modularity may emerge as a by-product of some trait. We here ask whether this last scenario may play a role in genome-scale metabolic networks that need to sustain life in one or more chemical environments. For such networks, we define a network module as a maximal set of reactions that are fully coupled, i.e., whose fluxes can only vary in fixed proportions. This definition overcomes limitations of purely graph based analyses of metabolism by exploiting the functional links between reactions. We call a metabolic network viable in a given chemical environment if it can synthesize all of an organism's biomass compounds from nutrients in this environment. An organism's metabolism is highly versatile if it can sustain life in many different chemical environments. We here ask whether versatility affects the modularity of metabolic networks.

- 1. Max Planck Institute for Mathematics in the Sciences (MPI-MIS), Max-Planck-Institut
- 3. Department of Biochemistry, University of Zurich
- 4. Swiss Institute of Bioinformatics (SIB), Swiss Institute of Bioinformatics
- 5. Santa Fe Institute, Santa Fe Institute
- 6. Laboratoire de Génétique Végétale du Moulon, Université Paris XI - Paris Sud

## Erratum: Anderson localization of expanding Bose-Einstein condensates in random potentials {Phys. Rev. Lett. 98, 210401 (2007)}

### Sanchez-Palencia, L., Clement, D., Lugan, P., Bouyer, P., Shlyapnikov, G.V., Aspect, A.

#### Physical Review Letters106 (2011) 149901

## Exact mean field inference in asymmetric kinetic Ising systems

### M. Mezard

^{1}, J. Sakellariou^{1}#### Journal of statistical mechanics-theory and experiment (2011) L07001

We develop an elementary mean field approach for fully asymmetric kinetic Ising models, which can be applied to a single instance of the problem. In the case of the asymmetric SK model this method gives the exact values of the local magnetizations and the exact relation between equal-time and time-delayed correlations. It can also be used to solve efficiently the inverse problem, i.e. determine the couplings and local fields from a set of patterns, also in cases where the fields and couplings are time-dependent. This approach generalizes some recent attempts to solve this dynamical inference problem, which were valid in the limit of weak coupling. It provides the exact solution to the problem also in strongly coupled problems. This mean field inference can also be used as an efficient approximate method to infer the couplings and fields in problems which are not infinite range, for instance in diluted asymmetric spin glasses.

## Excursions of diffusion processes and continued fractions

### Alain Comtet

^{1, 2}, Yves Tourigny^{3}#### Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

**47**(2011) 850-874It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.

- 1. Unite mixte de service de l'institut Henri Poincaré (UMSIHP), CNRS : UMS839 – Université Paris VI - Pierre et Marie Curie
- 3. School of Mathematics, University of Bristol

## Extreme Value Statistics Distributions in Spin Glasses

### Michele Castellana

^{1, 2}, Aurelien Decelle^{1}, Elia Zarinelli^{1}#### Physical Review Letters

**107**(2011) 275701We study the probability distribution of the pseudo-critical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick (SK) and the Edwards-Anderson (EA) model. In both cases, we put in evidence the underlying connection between the fluctuations of the pseudo-critical point and and the Extreme Value Statistics of random variables. For the SK model, both with Gaussian and binary couplings, the distribution of the pseudo-critical temperature is found to be the Tracy-Widom distribution. For the EA model, the distribution is found to be the Gumbel distribution. Being the EA model representative of uniaxial magnetic materials with quenched disorder like $Fe_{0.5} Mn_{0.5} Ti O_3$ or $Eu_{0.5} Ba_{0.5} Mn O_3$, its pseudo-critical point distribution should be a priori experimentally accessible.

- 2. Dipartimento di Fisica and INFM, Università degli studi di Roma I - La Sapienza

**2**)## Fermionic trimers in spin-dependent optical lattices

### Giuliano Orso

^{1}, Evgeni Burovski^{2}, Thierry Jolicoeur^{2}#### Comptes Rendus Physique

**12**(2011) 39-46We investigate the formation of three-body bound states (trimers) in two-component Fermi gases confined in one dimensional optical lattice with spin-dependent tunneling rates. The binding energy and the effective mass of the trimer are obtained from the solution of the Mattis integral equation generalized to the case of unequal Bloch masses. We show that this equation admits multiple solutions corresponding to excited bound states, which are only stable for large mass asymmetry.

- 1. Matériaux et Phénomènes Quantiques (MPQ), CNRS : UMR7162 – CNRS : FR2437 – Université Paris VII - Paris Diderot

## Field Theory of Fluctuations in Glasses

### Silvio Franz

^{1}, Giorgio Parisi^{2}, Federico Ricci-Tersenghi^{2}, Tommaso Rizzo^{2}#### The European Physical Journal E

**34**(2011) 102We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of 'self-induced disorder' in the initial condition of the dynamics. It follows that heterogeneites can be describes through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations.

- 2. Dipartimento di Fisica and INFM, Università degli studi di Roma I - La Sapienza

## Genome-Wide Crossover Distribution in <em>Arabidopsis thaliana </em>Meiosis Reveals Sex-Specific Patterns along Chromosomes

### Giraut, L., Falque, M., Drouaud, J., Pereira, L., Martin, O.C., Mezard, C.

#### PLoS genetics7 (2011) e1002354

## Geometry and material effects in Casimir physics – Scattering theory

### Sahand Jamal Rahi

^{1, 2}, Thorsten Emig^{3}, Robert L. Jaffe^{1}#### Casimir Physics (2011) vol. 834, 129-174

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, to nonzero temperatures, and to spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. This approach, which combines methods of statistical physics and scattering theory, is well suited to analyze many diverse phenomena. We illustrate its power and versatility by a number of examples, which show how the interplay of geometry and material properties helps to understand and control Casimir forces. We also examine whether electrodynamic Casimir forces can lead to stable levitation. Neglecting permeabilities, we prove that any equilibrium position of objects subject to such forces is unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.

- 1. Department of Physics, Massachusetts Institute of Technology
- 2. Center for Studies in Physics and Biology, The Rockefeller University

## Group testing with random pools: optimal two-stage algorithms

### Mezard, M., Toninelli, C.

#### IEEE Transactions on Information Theory57 (2011) 1736-1745

Details## Highest weight Macdonald and Jack Polynomials

### Th. Jolicoeur

^{1}, Jean-Gabriel Luque^{2}#### Journal of Physics A Mathematical and Theoretical, 44 (2011) 055204

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.

- 2. Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut National des Sciences Appliquées (INSA) - Rouen – Université du Havre – Université de Rouen : EA4108

## How many eigenvalues of a Gaussian random matrix are positive?

### Satya N. Majumdar

^{1}, Céline Nadal^{1}, Antonello Scardicchio^{2, 3}, Pierpaolo Vivo^{2}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**83**(2011) 041105We study the probability distribution of the index ${\mathcal N}_+$, i.e., the number of positive eigenvalues of an $N\times N$ Gaussian random matrix. We show analytically that, for large $N$ and large $\mathcal{N}_+$ with the fraction $0\le c=\mathcal{N}_+/N\le 1$ of positive eigenvalues fixed, the index distribution $\mathcal{P}({\mathcal N}_+=cN,N)\sim\exp[-\beta N^2 \Phi(c)]$ where $\beta$ is the Dyson index characterizing the Gaussian ensemble. The associated large deviation rate function $\Phi(c)$ is computed explicitly for all $0\leq c \leq 1$. It is independent of $\beta$ and displays a quadratic form modulated by a logarithmic singularity around $c=1/2$. As a consequence, the distribution of the index has a Gaussian form near the peak, but with a variance $\Delta(N)$ of index fluctuations growing as $\Delta(N)\sim \log N/\beta\pi^2$ for large $N$. For $\beta=2$, this result is independently confirmed against an exact finite $N$ formula, yielding $\Delta(N)= \log N/2\pi^2 +C+\mathcal{O}(N^{-1})$ for large $N$, where the constant $C$ has the nontrivial value $C=(\gamma+1+3\log 2)/2\pi^2\simeq 0.185248...$ and $\gamma=0.5772...$ is the Euler constant. We also determine for large $N$ the probability that the interval $[\zeta_1,\zeta_2]$ is free of eigenvalues. Part of these results have been announced in a recent letter [\textit{Phys. Rev. Lett.} {\bf 103}, 220603 (2009)].

- 2. The Abdus Salam International Centre for Theoretical Physics, ICTP Trieste
- 3. Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (INFN, Sezione di Trieste), INFN

**6**)## Hyperbolic disordered ensembles of random matrices

### O. Bohigas

^{1}, M. P. Pato^{2}#### Physical Review E

**84**(2011) 031121Using the simple procedure, recently introduced, of dividing Gaussian matrices by a positive random variable, a family of random matrices is generated characterized by a behavior ruled by the generalized hyperbolic distribution. The spectral density evolves from the semi-circle law to a Gaussian-like behavior while concomitantly the local fluctuations show a transition from the Wigner-Dyson to the Poisson statistics. Long range statistics such as number variance exhibit large fluctuations typical of non-ergodic ensembles.

- 2. Instituto de Fisica, Universidade de São Paulo

## Integrable random matrix ensembles

### E. Bogomolny

^{1}, O. Giraud^{1}, C. Schmit^{1}#### Nonlinearity

**24**(2011) 3179-3213We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with a random distribution of momenta and coordinates of the particles. The Lax matrices of these systems yield random matrix ensembles whose joint distribution of eigenvalues can be calculated analytically thanks to integrability of the underlying system. Formulas for spacing distributions and level compressibility are obtained for various instances of such ensembles.

## Interaction regimes for oppositely charged plates with multivalent counterions

### Fabien Paillusson

^{1}, Emmanuel Trizac^{2}#### Physical Review E

**84**(2011) 011407Within a mean field treatment of the interaction between two oppositely charged plates in a salt free solution, the distance at which a transition from an attractive to a repulsive regime appears can be computed analytically. The mean field description however breaks down under strong coulombic couplings, that can be achieved at room temperature with multivalent counter-ions and highly charged surfaces. Making use of the contact theorem and simple physical arguments, we propose explicit expressions for the equation of state in several situations at short distances. The possibility of Bjerrum pair formation is addressed and is shown to have profound consequences on the interactions. To complete the picture, we finally consider the large distance limit, from which schematic phase diagrams discriminating attractive from repulsive regions can be proposed.

- 1. Dept Chem., University of Cambridge

**2**)## Kondo effect and mesoscopic fluctuations

### Ullmo, D., Burdin, S., Liu, D.E., Baranger, H.U.

#### Pramana Journal of Physics77 (2011) 769-779

Details## Large deviations of the maximal eigenvalue of random matrices

### Gaëtan Borot

^{1}, Bertrand Eynard^{1}, Satya N. Majumdar^{2}, Céline Nadal^{2}#### Journal of Statistical Mechanics: Theory and Experiment (2011) P11024

We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called 'loop equations'). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.

- 1. Institut de Physique Théorique (ex SPhT) (IPHT), CNRS : URA2306 – CEA : DSM/IPHT

## Learning and structure of neuronal networks

### Kolwankar, K.M., Ren, Q.S., Samal, A., Jost, J.

#### Pramana Journal of physics77 (2011) 817-826

Details## Linearization effect in multifractal analysis: Insights from the Random Energy Model

### Florian Angeletti

^{1}, Marc Mézard^{2}, Eric Bertin^{1}, Patrice Abry^{1}#### Physica D: Nonlinear Phenomena

**240**, 16 (2011) 1245-1253The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of disordered systems, notably from the analysis of the so-called Random Energy Model. Considering a standard multifractal process (compound Poisson motion), chosen as a simple representative example, we show: i) the existence of a critical order $q^*$ beyond which moments, though finite, cannot be estimated through empirical averages, irrespective of the sample size of the observation; ii) that multifractal exponents necessarily behave linearly in $q$, for $q > q^*$. Tayloring the analysis conducted for the Random Energy Model to that of Compound Poisson motion, we provide explicative and quantitative predictions for the values of $q^*$ and for the slope controlling the linear behavior of the multifractal exponents. These quantities are shown to be related only to the definition of the multifractal process and not to depend on the sample size of the observation. Monte-Carlo simulations, conducted over a large number of large sample size realizations of compound Poisson motion, comfort and extend these analyses.

- 1. Laboratoire de Physique de l'ENS Lyon (Phys-ENS), CNRS : UMR5672 – École Normale Supérieure - Lyon

**1**)## Long-range steady state density profiles induced by localized drive

### Tridib Sadhu

^{1}, Satya N. Majumdar^{2}, David Mukamel^{1}#### Physical Review E

**84**(2011) 051136We show that the presence of a localized drive in an otherwise diffusive system results in steady-state density and current profiles that decay algebraically to their global average value, away from the drive in two or higher dimensions. An analogy to an electrostatic problem is established, whereby the density profile induced by a driving bond maps onto the electrostatic potential due to an electric dipole located along the bond. The dipole strength is proportional to the drive, and is determined self-consistently by solving the electrostatic problem. The profile resulting from a localized configuration of more than one driving bond can be straightforwardly determined by the superposition principle of electrostatics. This picture is shown to hold even in the presence of exclusion interaction between particles.

- 1. Weizmann Institute, Weizmann Institut

## Mean-field behavior of the negative-weight percolation model on random regular graphs

### O. Melchert

^{1}, A. K. Hartmann^{1}, M. Mezard^{2}#### Physical Review E

**84**(2011) 041106We investigate both analytically and numerically the ensemble of minimum-weight loops and paths in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the mean-field behavior of this model. The analytical study is based on a conjectured equivalence with the problem of self-avoiding walks in a random medium. The numerical study is based on a mapping to a standard minimum-weight matching problem for which fast algorithms exist. Both approaches yield results which are in agreement, on the location of the phase transition, on the value of critical exponents, and on the absence of any sizeable indications of a glass phase. By these results, the previously conjectured upper critical dimension of d_u=6 is confirmed.

- 1. Institute of Physics, University of Oldenburg

## Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder

### Arthur Lavarélo

^{1}, Guillaume Roux^{1}, Nicolas Laflorencie^{2}#### Physical Review B

**84**(2011) 144407The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by strong-coupling and mean-field analysis. Interestingly, this model displays remarkable features, bridging the physics of the J_1-J_2 chain and of the unfrustated ladder. The phase diagram as a function of the transverse coupling J_{\perp} and the frustration J_2 exhibits an Ising transition between a columnar phase of dimers and the usual rung-singlet phase of two-leg ladders. The transition is driven by resonating valence bond fluctuations in the singlet sector while the triplet spin gap remains finite across the transition. In addition, frustration brings incommensurability in the real-space spin correlation functions, the onset of which evolves smoothly from the J_1-J_2 chain value to zero in the large-J_{\perp} limit. The onset of incommensurability in the spin structure-factor and in the dispersion relation is also analyzed. The physics of the frustrated rung-singlet phase is well understood using perturbative expansions and mean-field theories in the large-J_{\perp} limit. Lastly, we discuss the effect of the non-trivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds which are currently investigated, such as BiCu_2PO_6, is eventually addressed.

- 2. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III

**5**)## Modeling microevolution in a changing environment: The evolving quasispecies and the Diluted Champion Process

### Ginestra Bianconi

^{1}, Davide Fichera^{2}, Silvio Franz^{2}, Luca Peliti^{3}#### Journal of Statistical Mechanics: Theory and Experiment (2011) P08022

Several pathogens use evolvability as a survival strategy against acquired immunity of the host. Despite their high variability in time, some of them exhibit quite low variability within the population at any given time, a somehow paradoxical behavior often called the evolving quasispecies. In this paper we introduce a simplified model of an evolving viral population in which the effects of the acquired immunity of the host are represented by the decrease of the fitness of the corresponding viral strains, depending on the frequency of the strain in the viral population. The model exhibits evolving quasispecies behavior in a certain range of its parameters, ans suggests how punctuated evolution can be induced by a simple feedback mechanism.

- 1. Department of physics, Northeastern University, Northeastern University
- 3. Dipartimento di Scienze Fisiche, Università degli studi di Napoli Federico II

## Motifs emerge from function in model gene regulatory networks

### Z. Burda

^{1}, A. Krzywicki^{2}, O. C. Martin^{3, 4}, M. Zagorski^{1}#### Proceedings of the National Academy of Sciences

**108**(2011) 17263Gene regulatory networks arise in all living cells, allowing the control of gene expression patterns. The study of their topology has revealed that certain subgraphs of interactions or 'motifs' appear at anomalously high frequencies. We ask here whether this phenomenon may emerge because of the functions carried out by these networks. Given a framework for describing regulatory interactions and dynamics, we consider in the space of all regulatory networks those that have a prescribed function. Monte Carlo sampling is then used to determine how these functional networks lead to specific motif statistics in the interactions. In the case where the regulatory networks are constrained to exhibit multi-stability, we find a high frequency of gene pairs that are mutually inhibitory and self-activating. In contrast, networks constrained to have periodic gene expression patterns (mimicking for instance the cell cycle) have a high frequency of bifan-like motifs involving four genes with at least one activating and one inhibitory interaction.

- 1. Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagellonian University
- 2. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud
- 4. Génétique Végétale (GV), CNRS : UMR8120 – Institut national de la recherche agronomique (INRA) : UMR0320 – Université Paris XI - Paris Sud – AgroParisTech

**2**)## Multimer formation in 1D two-component gases and trimer phase in the asymmetric attractive Hubbard model

### Guillaume Roux

^{1}, Evgeni Burovski^{2}, Thierry Jolicoeur^{1}#### Physical Review A: Atomic, Molecular and Optical Physics

**83**(2011) 053618We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multi-particle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the novel phase. The effective physics of the trimer gas is as well studied. Lastly, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.

- 2. Physics Department, Lancaster University

**5**)## Non-equilibrium Casimir forces: Spheres and sphere-plate

### Matthias Krüger

^{1}, Thorsten Emig^{2}, Giuseppe Bimonte^{3}, Mehran Kardar^{1}#### Europhysics Letters

**95**, 2 (2011) 21002We discuss non-equilibrium extensions of the Casimir force (due to electromagnetic fluctuations), where the objects as well as the environment are held at different temperatures. While the formalism we develop is quite general, we focus on a sphere in front of a plate, as well as two spheres, when the radius is small compared to separation and thermal wavelengths. In this limit the forces can be expressed analytically in terms of the lowest order multipoles, and corroborated with results obtained by diluting parallel plates of vanishing thickness. Non-equilibrium forces are generally stronger than their equilibrium counterpart, and may oscillate with separation (at a scale set by material resonances). For both geometries we obtain stable points of zero net force, while two spheres may have equal forces in magnitude and direction resulting in a self-propelling state.

- 1. Department of Physics, Massachusetts Institute of Technology
- 3. Dipartimento di Scienze Fisiche, Universita di Napoli Federico II

**11**)## Non-equilibrium electromagnetic fluctuations: Heat transfer and interactions

### Matthias Krüger

^{1}, Thorsten Emig^{2}, Mehran Kardar^{1}#### Physical Review Letters

**106**(2011) 210404The Casimir force between arbitrary objects in equilibrium is related to scattering from individual bodies. We extend this approach to heat transfer and Casimir forces in non-equilibrium cases where each body, and the environment, is at a different temperature. The formalism tracks the radiation from each body and its scatterings by the other objects. We discuss the radiation from a cylinder, emphasizing its polarized nature, and obtain the heat transfer between a sphere and a plate, demonstrating the validity of proximity transfer approximation at close separations and arbitrary temperatures.

- 1. Department of Physics, Massachusetts Institute of Technology

**30**)## Non-equilibrium phase transition in a sheared granular mixture

### V. Garzo

^{1}, E. Trizac^{2}#### Europhysics Letters

**94**, 5 (2011) 50009The dynamics of an impurity (or tracer particle) immersed in a dilute granular gas under uniform shear flow is investigated. A non-equilibrium phase transition is identified from an exact solution of the inelastic Boltzmann equation for a granular binary mixture in the tracer limit, where the impurity carries either a vanishing (disordered phase) or a finite (ordered phase) fraction of the total kinetic energy of the system. In the disordered phase, the granular temperature ratio (impurity 'temperature' over that of the host fluid) is finite, while it diverges in the ordered phase. To correctly capture this extreme violation of energy equipartition, we show that the picture of an impurity enslaved to the host fluid is insufficient.

- 1. Departamento de Fisica, Universidad de Extremadura

## Non-intersecting Brownian walkers and Yang-Mills theory on the sphere

### Forrester, P.J., Majumdar, S.N., Schehr, G.

#### Nuclear Physics B844 (2011) 500-526

Details## On the solution of a `solvable’ model of an ideal glass of hard spheres displaying a jamming transition

### Marc Mezard

^{1}, Giorgio Parisi^{2}, Marco Tarzia^{3}, Francesco Zamponi^{4}#### Journal of statistical mechanics-theory and experiment (2011) P03002

We discuss the analytical solution through the cavity method of a mean field model that displays at the same time an ideal glass transition and a set of jamming points. We establish the equations describing this system, and we discuss some approximate analytical solutions and a numerical strategy to solve them exactly. We compare these methods and we get insight into the reliability of the theory for the description of finite dimensional hard spheres.

- 2. Dipartimento di Fisica, Università Roma I
- 3. Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
- 4. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

**1**)## Parametric Excitation of a 1D Gas in Integrable and Nonintegrable Cases

### M. Colomé-Tatché

^{1}, D. S. Petrov^{2, 3}#### Physical Review Letters

**106**(2011) 125302We study the response of a highly excited 1D gas with pointlike interactions to a periodic modulation of the coupling constant. We calculate the corresponding dynamic structure factors and show that their low-frequency behavior differs dramatically for integrable and nonintegrable models. Nonintegrable systems are sensitive to excitations with frequencies as low as the mean level spacing, whereas much higher frequencies are required to excite an integrable system. This effect can be used as a probe of integrability for mesoscopic 1D systems and can be observed experimentally by measuring the heating rate of a parametrically excited gas.

- 1. Institut fur Theoretische Physik, Leibniz Universität Hannover
- 3. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow

**2**)## Perturbation approach to multifractal dimensions for certain critical random matrix ensembles

### E. Bogomolny

^{1}, O. Giraud^{1}#### Physical Review E

**84**(2011) 036212Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the critical banded random matrix ensemble extensively discussed in the literature. For certain ensembles, the leading-order term for weak multifractality can be calculated within standard perturbation theory. For other models such a direct approach requires modifications which are briefly discussed. Our analytical formulas are in good agreement with numerical calculations.

**7**)## Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries

### Kay Jörg Wiese

^{1}, Satya N. Majumdar^{2}, Alberto Rosso^{2}#### Physical Review E

**83**(2011) 061141Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations ~ t^{2H} + s^{2H} - |t-s|^{2H}, where H, with 0 0 (near the absorbing boundary), while R(y) ~ y^gamma exp(-y^2/2) as y -> oo, with phi = 1 - 4 epsilon + O(epsilon^2) and gamma = 1 - 2 epsilon + O(epsilon^2). Our epsilon-expansion result confirms the scaling relation phi = (1-H)/H proposed in Ref. [28]. We verify our findings via numerical simulations for H = 2/3. The tools developed here are versatile, powerful, and adaptable to different situations.

- 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

## Phase diagram of hard-core bosons on clean and disordered 2-leg ladders: Mott insulator – Luttinger liquid – Bose glass

### François Crépin

^{1}, Nicolas Laflorencie^{1}, Guillaume Roux^{2}, Pascal SIMON^{1}#### Physical Review B

**84**(2011) 054517One dimensional free-fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depends on the so-called Jordan-Wigner string, real-space observables are similar for free-fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed, and leads to a totally different physics between free-fermions and hard-core bosons. Using a combination of analytical (strong coupling, field theory, renormalization group) and numerical (quantum Monte Carlo, density-matrix renormalization group) approaches, we study the apparently simple but non-trivial model of hard-core bosons hopping in a two-leg ladder geometry. At half-filling, while a band insulator appears for fermions at large interchain hopping tperp >2t only, a Mott gap opens up for bosons as soon as tperp\neq0 through a Kosterlitz-Thouless transition. Away from half-filling, the situation is even more interesting since a gapless Luttinger liquid mode emerges in the symmetric sector with a non-trivial filling-dependent Luttinger parameter 1/2\leq Ks \leq 1. Consequences for experiments in cold atoms, spin ladders in a magnetic field, as well as disorder effects are discussed. In particular, a quantum phase transition is expected at finite disorder strength between a 1D superfluid and an insulating Bose glass phase.

- 1. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud

**5**)## Phase transition in the detection of modules in sparse networks

### Aurelien Decelle

^{1}, Florent Krzakala^{2}, Cristopher Moore^{3, 4}, Lenka Zdeborová^{5}#### Physical Review Letters

**107**(2011) 065701We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks. Our results are also applicable to detection of functional modules, partitions, and colorings in noisy planted models. Using a cavity method analysis, we unveil a phase transition from a region where the original group assignment is undetectable to one where detection is possible. In some cases, the detectable region splits into an algorithmically hard region and an easy one. Our approach naturally translates into a practical algorithm for detecting modules in sparse networks, and learning the parameters of the underlying model.

- 2. Laboratoire de Physico-Chimie Théorique (LPCT), CNRS : UMR7083 – ESPCI ParisTech
- 3. Department of Computer Science - UNM, University of New Mexico
- 4. Sante Fe Institute (SFI), -
- 5. Institut de Physique Théorique (ex SPhT) (IPHT), CNRS : URA2306 – CEA : DSM/IPHT

**11**)## Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with many transverse modes

### Kedar Damle

^{1}, Satya N. Majumdar^{2}, Vikram Tripathi^{1}, Pierpaolo Vivo^{2}#### Physical Review Letters

**107**(2011) 177206We compute analytically the full distribution of Andreev conductance $G_{\mathrm{NS}}$ of a metal-superconductor interface with a large number $N_c$ of transverse modes, using a random matrix approach. The probability distribution $\mathcal{P}(G_{\mathrm{NS}},N_c)$ in the limit of large $N_c$ displays a Gaussian behavior near the average value $= (2-\sqrt{2}) N_c$ and asymmetric power-law tails in the two limits of very small and very large $G_{\mathrm{NS}}$. In addition, we find a novel third regime sandwiched between the central Gaussian peak and the power law tail for large $G_{\mathrm{NS}}$. Weakly non-analytic points separate these four regimes---these are shown to be consequences of three phase transitions in an associated Coulomb gas problem.

- 1. Tata Institute of Fundamental Research, Tata Institute

**3**)## Phenotypic plasticity can facilitate adaptive evolution in gene regulatory circuits

### Espinosa-Soto, C., Martin, O.C., Wagner, A.

#### BMC Evolutionary Biology11 (2011) 5

## Phenotypic robustness can increase phenotypic variability after non-genetic perturbations in gene regulatory circuits

### Carlos Espinosa-Soto

^{1, 2}, Olivier C. Martin^{3, 4}, Andreas Wagner^{1, 2, 5}#### Journal of Evolutionary Biology

**24**(2011) 1284-1297Non-genetic perturbations, such as environmental change or developmental noise, can induce novel phenotypes. If an induced phenotype confers a fitness advantage, selection may promote its genetic stabilization. Non-genetic perturbations can thus initiate evolutionary innovation. Genetic variation that is not usually phenotypically visible may play an important role in this process. Populations under stabilizing selection on a phenotype that is robust to mutations can accumulate such variation. After non-genetic perturbations, this variation can become a source of new phenotypes. We here study the relationship between a phenotype's robustness to mutations and a population's potential to generate novel phenotypic variation. To this end, we use a well-studied model of transcriptional regulation circuits. Such circuits are important in many evolutionary innovations. We find that phenotypic robustness promotes phenotypic variability in response to non-genetic perturbations, but not in response to mutation. Our work suggests that non-genetic perturbations may initiate innovation more frequently in mutationally robust gene expression traits.

- 1. Department of Biochemistry, University of Zurich
- 2. Swiss Institute of Bioinformatics (SIB), Swiss Institute of Bioinformatics
- 4. Laboratoire de Génétique Végétale du Moulon, Université Paris XI - Paris Sud
- 5. Santa Fe Institute, Santa Fe Institute

## Polar Phase of 1D Bosons with Large Spin

### G. V. Shlyapnikov

^{1}, A. M. Tsvelik^{2}#### New Journal of Physics

**13**(2011) 065012Spinor ultracold gases in one dimension represent an interesting example of strongly correlated quantum fluids. They have a rich phase diagram and exhibit a variety of quantum phase transitions. We consider a one-dimensional spinor gas of bosons with a large spin $S$. A particular example is the gas of chromium atoms (S=3), where the dipolar collisions efficiently change the magnetization and make the system sensitive to the linear Zeeman effect. We argue that in one dimension the most interesting effects come from the pairing interaction. If this interaction is negative, it gives rise to a (quasi)condensate of singlet bosonic pairs with an algebraic order at zero temperature, and for $(2S+1)\gg 1$ the saddle point approximation leads to physically transparent results. Since in one dimension one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of magnetic field there is only one gapless mode corresponding to phase fluctuations of the pair quasicondensate. Once the magnetic field exceeds the gap another condensate emerges, namely the quasicondensate of unpaired bosons with spins aligned along the magnetic field. The spectrum then contains two gapless modes corresponding to the singlet-paired and spin-aligned unpaired bose-condensed particles, respectively. At T=0 the corresponding phase transition is of the commensurate-incommensurate type.

- 2. Department of Condensed Matter Physics and Material Science, Brookhaven National Laboratory

## Polar phase of one-dimensional bosons with large spin

### Shlyapnikov, G.V., Tsvelik, A.M.

#### New Journal of Physics13 (2011) 065012

Details## Quantum Monte Carlo calculation of the zero-temperature phase diagram of the two-component fermionic hard-core gas in two dimensions

### N. D. Drummond

^{1, 2}, N. R. Cooper^{1}, R. J. Needs^{1}, G. V. Shlyapnikov^{3, 4}#### Physical Review B

**83**(2011) 195429Motivated by potential realizations in cold-atom or cold-molecule systems, we have performed quantum Monte Carlo simulations of two-component gases of fermions in two dimensions with hard-core interactions. We have determined the gross features of the zero-temperature phase diagram, by investigating the relative stabilities of paramagnetic and ferromagnetic fluids and crystals. We have also examined the effect of including a pairwise, long-range r^(-3) potential between the particles. Our most important conclusion is that there is no region of stability for a ferromagnetic fluid phase, even if the long-range interaction is present. We also present results for the pair-correlation function, static structure factor, and momentum density of two-dimensional hard-core fluids.

- 1. TCM Group, Cavendish Laboratory, Cavendish Laboratory Cambridge
- 2. Department of Physics, Lancaster University
- 4. Van der Waals-Zeeman Institute, University of Amsterdam

**5**)## Randomizing genome-scale metabolic networks

### Areejit Samal

^{1, 2}, Olivier C. Martin^{2, 3}#### PLoS ONE

**6**(2011) e22295Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have 'unusual' properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the network is not statistically different from expected in a motivated ensemble. However, when dealing with metabolic networks, the randomization of the network using edge exchange generates fictitious reactions that are biochemically meaningless. Here we provide several natural ensembles of randomized metabolic networks. A first constraint is to use valid biochemical reactions. Further constraints correspond to imposing appropriate functional constraints. We explain how to perform these randomizations with the help of Markov Chain Monte Carlo (MCMC) and show that they allow one to approach the properties of biological metabolic networks. The implication of the present work is that the observed global structural properties of real metabolic networks are likely to be the consequence of simple biochemical and functional constraints.

- 1. Max Planck Institute for Mathematics in the Sciences (MPI-MIS), Max-Planck-Institut
- 3. Laboratoire de Génétique Végétale du Moulon, Université Paris XI - Paris Sud

## Real space Renormalization Group analysis of a non-mean field spin-glass

### Michele Castellana

^{1, 2}#### Europhysics Letters

**95**, 4 (2011) 47014A real space Renormalization Group approach is presented for a non-mean field spin-glass. This approach has been conceived in the effort to develop an alternative method to the Renormalization Group approaches based on the replica method. Indeed, non-perturbative effects in the latter are quite generally out of control, in such a way that these approaches are non-predictive. On the contrary, we show that the real space method developed in this work yields precise predictions for the critical behavior and exponents of the model.

- 2. Dipartimento di Fisica and INFM, Università degli studi di Roma I - La Sapienza

## Renormalization-group computation of the critical exponents of hierarchical spin glasses: Large-scale behavior and divergence of the correlation length

### Castellana, M., Parisi, G.

#### Physical Review E83 (2011) 041134

## Role of the Tracy-Widom distribution in the finite-size fluctuations of the critical temperature of the Sherrington-Kirkpatrick spin glass

### Michele Castellana

^{1, 2}, Elia Zarinelli^{1}#### Physical Review B

**84**(2011) 144417We investigate the finite-size fluctuations due to quenched disorder of the critical temperature of the Sherrington-Kirkpatrick spin glass. In order to accomplish this task, we perform a finite-size analysis of the spectrum of the susceptibility matrix obtained via the Plefka expansion. By exploiting results from random matrix theory, we obtain that the fluctuations of the critical temperature are described by the Tracy-Widom distribution with a non-trivial scaling exponent 2/3.

- 2. Dipartimento di Fisica and INFM, Università degli studi di Roma I - La Sapienza

**3**)## Semiclassical magnetotransport in graphene n-p junctions

### Pierre Carmier

^{1, 2}, Caio Lewenkopf^{3}, Denis Ullmo^{1}#### Physical Review B

**84**(2011) 195428We provide a semiclassical description of the electronic transport through graphene n-p junctions in the quantum Hall regime. This framework is known to experimentally exhibit conductance plateaus whose origin is still not fully understood. In the magnetic regime (E < vF B), we show the conductance of excited states is essentially zero, while that of the ground state depends on the boundary conditions considered at the edge of the sample. In the electric regime (E > vF B), for a step-like electrostatic potential (abrupt on the scale of the magnetic length), we derive a semiclassical approximation for the conductance in terms of the various snake-like trajectories at the interface of the junction. For a symmetric configuration, the general result can be recovered using a simple scattering approach, providing a transparent analysis of the problem under study. We thoroughly discuss the semiclassical predicted behavior for the conductance and conclude that any approach using fully phase-coherent electrons will hardly account for the experimentally observed plateaus.

- 2. Institut Nanosciences et Cryogénie (ex DRFMC) (INAC), CEA : DSM/INAC
- 3. Instituto de Fisica, Universidade Federal Fluminense

**5**)## Shock statistics in higher-dimensional Burgers turbulence

### Pierre Le Doussal

^{1}, Alberto Rosso^{2}, Kay Jörg Wiese^{1}#### Europhysics Letters

**96**, 1 (2011) 14005We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated.

- 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

## Slow quench dynamics of a trapped one-dimensional Bose gas confined to an optical lattice

### Jean-Sebastien Bernier

^{1}, Guillaume Roux^{2}, Corinna Kollath^{1, 3}#### Physical Review Letters

**106**(2011) 200601We analyze the effect of a linear time-variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible onsite particle distribution are studied as a function of the ramp time using time-dependent exact diagonalization and density-matrix renormalization group techniques. We find that the dynamics of a trapped system typically display two regimes: for long ramp times, the dynamics are governed by density redistribution, while at short ramp times, local dynamics dominate as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the non-trivial scaling of the energy absorbed with the ramp time.

- 1. Centre de Physique Théorique (CPHT), CNRS : UMR7644 – Polytechnique - X
- 3. Département de Physique Théorique, University of Geneva

**14**)## Special section on constraint satisfaction problems and message passing algorithms

### Mezard, M., Tetali, P.

#### SIAM Journal on Discrete Mathematics25 (2011) 733-735

Details## Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field

### Pierre Bouillot

^{1}, Corinna Kollath^{1, 2}, Andreas M. Läuchli^{3}, Mikhail Zvonarev^{4, 5}, Benedikt Thielemann^{6}, Christian Rüegg^{7}, Edmond Orignac^{8}, Roberta Citro^{9}, Martin Klanjsek^{10, 11}, Claude Berthier^{11}, Mladen Horvatic^{11}, Thierry Giamarchi^{1}#### Physical Review B

**83**(2011) 054407We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (C5H12N)2CuBr4 (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.

- 1. DPMC-Manep, Université de Genève
- 2. Centre de Physique Théorique (CPHT), CNRS : UMR7644 – Polytechnique - X
- 3. Max Planck Institute Physik Komplexer Systems, Max-Planck-Institut
- 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 5. Department of Physics, University of Harvard
- 6. Paul Scherrer Institut (PSI), Aucune
- 7. London Centre for Nanotechnology and Department of Physics and Astronomy,, University College of London (UCL)
- 8. Laboratoire de Physique de l'ENS Lyon (Phys-ENS), CNRS : UMR5672 – École Normale Supérieure - Lyon
- 9. Dipartamento di Fisica "E. R. Caianiello", Università degli studi di Salerno
- 10. Solid State Physics Department, Jozef Stefan Institute
- 11. Laboratoire National des Champs Magnétiques Intenses (LNCMI), CNRS : UPR3228

## Statistical Curse of the Second Half Rank

### Jean Desbois

^{1}, Stephane Ouvry^{1}, Alexios Polychronakos^{2}#### Journal of statistical mechanics-theory and experiment (2011) P01025

In competitions involving many participants running many races the final rank is determined by the score of each participant, obtained by adding its ranks in each individual race. The 'Statistical Curse of the Second Half Rank' is the observation that if the score of a participant is even modestly worse than the middle score, then its final rank will be much worse (that is, much further away from the middle rank) than might have been expected. We give an explanation of this effect for the case of a large number of races using the Central Limit Theorem. We present exact quantitative results in this limit and demonstrate that the score probability distribution will be gaussian with scores packing near the center. We also derive the final rank probability distribution for the case of two races and we present some exact formulae verified by numerical simulations for the case of three races. The variant in which the worst result of each boat is dropped from its final score is also analyzed and solved for the case of two races.

- 2. Physics Department, City College of New York

## Statistical distribution of quantum entanglement for a random bipartite state

### Celine Nadal

^{1}, Satya N Majumdar^{1}, Massimo Vergassola^{2}#### Journal of Statistical Physics

**142**(2011) 403-438We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping the problem to a random matrix model and then using a Coulomb gas method. We identify three different regimes in the entropy distribution, which correspond to two phase transitions in the associated Coulomb gas. The two critical points correspond to sudden changes in the shape of the Coulomb charge density: the appearance of an integrable singularity at the origin for the first critical point, and the detachement of the rightmost charge (largest eigenvalue) from the sea of the other charges at the second critical point. Analytical results are verified by Monte Carlo numerical simulations. A short account of some of these results appeared recently in Phys. Rev. Lett. {\bf 104}, 110501 (2010).

- 2. Institut Pasteur, Institut Pasteur de Paris

**11**)## Statistics of layered zigzags: a two-dimensional generalization of TASEP

### Mikhail Tamm

^{1}, Sergei K. Nechaev^{2, 3}, Satya N. Majumdar^{2}#### Journal of Physics A Mathematical and Theoretical

**44**(2011) 012002A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted minimal local height gradient. We demonstrate that the coarse-grained behavior of this model is described by the two-dimensional Kardar-Parisi-Zhang equation. The coefficients of different terms in this hydrodynamic equation can be derived from the steady state flow-density curve, the so called `fundamental' diagram. A conjecture concerning the analytical form of this flow-density curve is presented and is verified numerically.

- 1. Physics Department, Moscow State University
- 3. P. N. Lebedev Physical Institute, Russian Academy of Science

## Statistics of noncoding RNAs: alignment and secondary structure prediction

### S. K. Nechaev

^{1, 2, 3}, M. V. Tamm^{4}, O. V. Valba^{1, 5}#### Journal of Physics A Mathematical and Theoretical

**44**(2011) 195001A new statistical method of alignment of two heteropolymers which can form hierarchical cloverleaf-like secondary structures is proposed. This offers a new constructive algorithm for quantitative determination of binding free energy of two noncoding RNAs with arbitrary primary sequences. The alignment of ncRNAs differs from the complete alignment of two RNA sequences: in ncRNA case we align only the sequences of nucleotides which constitute pairs between two different RNAs, while the secondary structure of each RNA comes into play only by the combinatorial factors affecting the entropc contribution of each molecule to the total cost function. The proposed algorithm is based on two observations: i) the standard alignment problem is considered as a zero-temperature limit of a more general statistical problem of binding of two associating heteropolymer chains; ii) this last problem is generalized onto the sequences with hierarchical cloverleaf-like structures (i.e. of RNA-type). Taking zero-temperature limit at the very end we arrive at the desired 'cost function' of the system with account for entropy of side cactus-like loops. Moreover, we have demonstrated in detail how our algorithm enables to solve the 'structure recovery' problem. Namely, we can predict in zero-temperature limit the cloverleaf-like (i.e. secondary) structure of interacting ncRNAs by knowing only their primary sequences.

- 2. P. N. Lebedev Physical Institute, Russian Academy of Science
- 3. JV Poncelet Laboratory, Independant University
- 4. Physics Department, Moscow State University
- 5. Moscow Institute of Physics and Technology (MIPT), Moscow Institute of Physics and Technology

## Strong screening in the plum pudding model

### A. D. Chepelianskii

^{1}, F. Closa^{2}, E. Raphael^{2}, E. Trizac^{3}#### Europhysics Letters (EPL)

**94**(2011) 68010We study a generalized Thomson problem that appears in several condensed matter settings: identical point-charge particles can penetrate inside a homogeneously charged sphere, with global electro-neutrality. The emphasis is on scaling laws at large Coulombic couplings, and deviations from mean-field behaviour, by a combination of Monte Carlo simulations and an analytical treatment within a quasi-localized charge approximation, which provides reliable predictions. We also uncover a local overcharging phenomenon driven by ionic correlations alone.

- 1. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
- 2. Gulliver, UMR CNRS 7083, ESPCI ParisTech

## Strong-Coupling Theory of Counter-ions at Charged Plates

### L. Samaj

^{1}, E. Trizac^{2}#### Physical Review Letters

**106**(2011) 078301We present an analytical approach to the strong coupling regime of similarly and highly charged plates in the presence of counter-ions. The procedure is physically transparent and based on an exact expansion around the ground state formed by the two-dimensional Wigner crystal of counter-ions. The one plate problem is worked out, together with the two plates situation. Unlike previous approaches, the expansion is free of divergences, and is shown to be in excellent agreement with available data of Monte-Carlo simulations under strong Coulombic couplings. The present results shed light on the like-charge attraction regime.

- 1. Institute of Physics, Slovak Academy of Sciences

## Supersymmetric quantum mechanics with Levy disorder in one dimension

### Alain Comtet

^{1, 2}, Christophe Texier^{2, 3}, Yves Tourigny^{4}#### Journal of Statistical Physics

**145**(2011) 1291-1323We consider the Schroedinger equation with a supersymmetric random potential, where the superpotential is a Levy noise. We focus on the problem of computing the so-called complex Lyapunov exponent, whose real and imaginary parts are, respectively, the Lyapunov exponent and the integrated density of states of the system. In the case where the Levy process is non-decreasing, we show that the calculation of the complex Lyapunov exponent reduces to a Stieltjes moment problem, we ascertain the low-energy behaviour of the density of states in some generality, and relate it to the distributional properties of the Levy process. We review the known solvable cases, where the complex Lyapunov exponent can be expressed in terms of special functions, and discover a new one.

- 1. Unite mixte de service de l'institut Henri Poincaré (UMSIHP), CNRS : UMS839 – Université Paris VI - Pierre et Marie Curie
- 3. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
- 4. School of Mathematics, University of Bristol

**1**)## The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media

### Dimitrova, O., Mezard, M.

#### Journal of Statistical Mechanics(2011) P01020

Details## The convex hull for a random acceleration process in two dimensions

### Alexis Reymbaut, Satya N. Majumdar

^{1}, Alberto Rosso^{1}#### Journal of Physics A: Mathematical and Theoretical

**44**, 41 (2011) 415001We compute exactly the mean perimeter and the mean area of the convex hull of a random acceleration process of duration T in two dimensions. We use an exact mapping that relates, via Cauchy's formulae, the computation of the perimeter and the area of the convex hull of an arbitrary two dimensional stochastic process [x(t); y(t)] to the computation of the extreme value statistics of the associated one dimensional component process x(t). The latter can be computed exactly for the one dimensional random acceleration process even though the process in non-Markovian. Physically, our results are relevant in describing theaverage shape of a semi-flexible ideal polymer chain in two dimensions.

## The Zak phase and the existence of edge states in graphene

### P. Delplace

^{1}, D. Ullmo^{2}, G. Montambaux^{3}#### Physical Review B

**84**(2011) 195452We develop a method to predict the existence of edge states in graphene ribbons for a large class of boundaries. This approach is based on the bulk-edge correspondence between the quantized value of the Zak phase Z(k), which is a Berry phase across an appropriately chosen one-dimensional Brillouin zone, and the existence of a localized state of momentum k at the boundary of the ribbon. This bulk-edge correspondence is rigorously demonstrated for a one dimensional toy model as well as for graphene ribbons with zigzag edges. The range of k for which edge states exist in a graphene ribbon is then calculated for arbitrary orientations of the edges. Finally, we show that the introduction of an anisotropy leads to a topological transition in terms of the Zak phase, which modifies the localization properties at the edges. Our approach gives a new geometrical understanding of edge states, it con?firms and generalizes the results of several previous works.

- 1. Département de Physique, Université de Genève
- 3. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud

**6**)## Thermal noise and dephasing due to electron interactions in non-trivial geometries

### M. Treiber

^{1}, C. Texier^{2, 3}, O. M. Yevtushenko^{1}, J. von Delft^{1}, I. V. Lerner^{4}#### Physical Review B

**84**(2011) 054204We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered metals and give a microscopic derivation of the correlation function of the scalar electric potentials in real space. Starting from the interacting Hamiltonian for electrons in a metal and the random phase approximation, we find a relation between the correlation function of the electric potentials and the density fluctuations which is valid for arbitrary geometry and dimensionality. We show that the potential fluctuations are proportional to the solution of the diffusion equation, taken at zero frequency. As an example, we consider networks of quasi-1D disordered wires and give an explicit expression for the correlation function in a ring attached via arms to absorbing leads. We use this result in order to develop a theory of dephasing by electronic noise in multiply-connected systems.

- 1. Arnold Sommerfeld Center and Center for Nano-Science, Ludwig Maximilians Universität München
- 2. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
- 4. School of Physics and Astronomy, University of Birmingham

**2**)## Tkachenko modes and their damping in the vortex lattice regime of rapidly rotating bosons

### S. I. Matveenko

^{1, 2}, G. V. Shlyapnikov^{1, 3}#### Physical Review A: Atomic, Molecular and Optical Physics

**83**(2011) 033604We have found an exact analytical solution of the Bogoliubov-de Gennes equations for the Tkachenko modes of the vortex lattice in the lowest Landau level (LLL) in the thermodynamic limit at any momenta and calculated their damping rates. At finite temperatures both Beliaev and Landau damping leads to momentum independent damping rates in the low-energy limit, which shows that at sufficiently low energies Tkachenko modes become strongly damped. We then found that the mean square fluctuations of the density grow logarithmically at large distances, which indicates that the state is ordered in the vortex lattice only on a finite (although exponentially large) distance scale and introduces a low-momentum cut-off. Using this circumstance we showed that at finite temperatures the one-body density matrix undergoes an exponential decay at large distances.

- 2. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
- 3. Van der Waals-Zeeman Institute, University of Amsterdam

## Topological p_x+ip_y Superfluid Phase of Fermionic Polar Molecules

### J. Levinsen

^{1, 2}, N. R. Cooper^{1, 2}, G. V. Shlyapnikov^{1, 3}#### Physical Review A

**84**(2011) 013603We discuss the topological p_x+ip_y superfluid phase in a 2D gas of single-component fermionic polar molecules dressed by a circularly polarized microwave field. This phase emerges because the molecules may interact with each other via a potential V_0(r) that has an attractive dipole-dipole 1/r^3 tail, which provides p-wave superfluid pairing at fairly high temperatures. We calculate the amplitude of elastic p-wave scattering in the potential V_0(r) taking into account both the anomalous scattering due to the dipole-dipole tail and the short-range contribution. This amplitude is then used for the analytical and numerical solution of the renormalized BCS gap equation which includes the second order Gor'kov-Melik-Barkhudarov corrections and the correction related to the effective mass of the quasiparticles. We find that the critical temperature T_c can be varied within a few orders of magnitude by modifying the short-range part of the potential V_0(r). The decay of the system via collisional relaxation of molecules to dressed states with lower energies is rather slow due to the necessity of a large momentum transfer. The presence of a constant transverse electric field reduces the inelastic rate, and the lifetime of the system can be of the order of seconds even at 2D densities ~ 10^9 cm^{-2}. This leads to T_c of up to a few tens of nanokelvins and makes it realistic to obtain the topological p_x+ip_y phase in experiments with ultracold polar molecules.

- 2. TCM Group, Cavendish Laboratory, Cavendish Laboratory Cambridge
- 3. Van der Waals-Zeeman Institute, University of Amsterdam

**16**)## Trace formula for dielectric cavities II: Regular, pseudo-integrable, and chaotic examples

### E. Bogomolny

^{1}, N. Djellali^{2}, R. Dubertrand^{3}, I. Gozhyk^{2}, M. Lebental^{2}, C. Schmit^{1}, C. Ulysse^{4}, J. Zyss^{2}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**83**(2011) 036208Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [PRE, vol. 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudo-integrable (pentagon) and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simulations, and experiments based on organic micro-lasers.

- 2. Laboratoire de Photonique Quantique et Moléculaire (LPQM), CNRS : UMR8537 – École normale supérieure de Cachan - ENS Cachan
- 3. Institut fur Theoretische Physik, University of Heidelberg
- 4. Laboratoire de photonique et de nanostructures (LPN), CNRS : UPR20

## Universality versus material dependence of fluctuation forces between metallic wires

### Ehsan Noruzifar

^{1}, Thorsten Emig^{2}, Roya Zandi^{1}#### Physical Review A

**84**(2011) 042501We calculate the Casimir interaction between two parallel wires and between a wire and a metall plate. The dielectric properties of the objects are described by the plasma, Drude and perfect metal models. We find that at asymptotically large separation interactions involving plasma wires and/or plates are independent of the material properties, but depend on the dc conductivity $\sigma$ for Drude wires. Counterintuitively, at intermediate separations the interaction involving Drude wires can become independent of $\sigma$. At smaller separations, we compute the interaction numerically and observe an approach to the proximity approximation.

- 1. Department of Physics and Astronomy, University of California, Riverside

**8**)## Using affinity propagation for identifying subspecies among clonal organisms: lessons from <em>M. tuberculosis</em>

### Borile, C., Labarre, M., Franz, S., Sola, C., Refregier, G.

#### BMC Bioinformatics12 (2011) 224

Details## Wigner-Crystal Formulation of Strong-Coupling Theory for Counter-ions Near Planar Charged Interfaces

### L. Šamaj

^{1, 2}, E. Trizac^{2}#### Physical Review E

**84**(2011) 041401We present a new analytical approach to the strong electrostatic coupling regime (SC), that can be achieved equivalently at low temperatures, high charges, low dielectric permittivity etc. Two geometries are analyzed in detail: one charged wall first, and then, two parallel walls at small distances, that can be likely or oppositely charged. In all cases, one type of mobile counter-ions only is present, and ensures electroneutrality (salt free case). The method is based on a systematic expansion around the ground state formed by the two-dimensional Wigner crystal(s) of counter-ions at the plate(s). The leading SC order stems from a single-particle theory, and coincides with the virial SC approach that has been much studied in the last 10 years. The first correction has the functional form of the virial SC prediction, but the prefactor is different. The present theory is free of divergences and the obtained results, both for symmetrically and asymmetrically charged plates, are in excellent agreement with available data of Monte-Carlo simulations under strong and intermediate Coulombic couplings. All results obtained represent relevant improvements over the virial SC estimates. The present SC theory starting from the Wigner crystal and therefore coined Wigner SC, sheds light on anomalous phenomena like the counter-ion mediated like-charge attraction, and the opposite-charge repulsion.

- 1. Institute of Physics, Slovak Academy of Sciences