# LPTMS Publications

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## $\zeta$-regularised spectral determinants on metric graphs

### Christophe Texier

^{1, 2}#### Journal of Physics A Mathematical and Theoretical

**43**(2010) 425203Several general results for the spectral determinant of the Schrödinger operator on metric graphs are reviewed. Then, a simple derivation for the $\zeta$-regularised spectral determinant is proposed, based on the Roth trace formula. Two types of boundary conditions are studied: functions continuous at the vertices and functions whose derivative is continuous at the vertices. The $\zeta$-regularised spectral determinant of the Schrödinger operator acting on functions with the most general boundary conditions is conjectured in conclusion. The relation to the Ihara, Bass and Bartholdi formulae obtained for combinatorial graphs is also discussed.

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

**2**)## Area distribution and the average shape of a Lévy bridge

### Schehr, G., Majumdar, S.N.

#### Journal of Statistical Mechanics(2010) P08055

Details## Asymptotic mean density of sub-unitary ensemble

### E. Bogomolny

^{1}#### Journal of Physics A Mathematical and Theoretical

**43**(2010) 335102The large N limit of mean spectral density for the ensemble of NxN sub-unitary matrices derived by Wei and Fyodorov (J. Phys. A: Math. Theor. 41 (2008) 50201) is calculated by a modification of the saddle point method. It is shown that the result coincides with the one obtained within the free probability theory by Haagerup and Larsen (J. Funct. Anal. 176 (2000) 331).

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

## Breakdown of the superfluidity of a matter wave in a random environment

### M. Albert

^{1}, T. Paul^{2}, N. Pavloff^{2}, P. Leboeuf^{2}#### Physical Review A: Atomic, Molecular and Optical Physics

**82**(2010) 011602We consider a guided Bose-Einstein matter wave flowing through a disordered potential. We determine the critical velocity at which superfluidity is broken and compute its statistical properties. They are shown to be connected to extreme values of the random potential. Experimental implementations of this physics are discussed.

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

## Capillarity Theory for the Fly-Casting Mechanism

### E. Trizac

^{1}, Y. Levy^{2}, P. G. Wolynes^{3}#### Proceeding of the national academy of sciences

**107**(2010) 2746Biomolecular folding and function are often coupled. During molecular recognition events, one of the binding partners may transiently or partially unfold, allowing more rapid access to a binding site. We describe a simple model for this flycasting mechanism based on the capillarity approximation and polymer chain statistics. The model shows that flycasting is most effective when the protein unfolding barrier is small and the part of the chain which extends towards the target is relatively rigid. These features are often seen in known examples of flycasting in protein-DNA binding. Simulations of protein-DNA binding based on well-funneled native-topology models with electrostatic forces confirm the trends of the analytical theory.

- 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 2. Department of Structural Biology, Weizmann Institute
- 3. Department of Chemistry and Biochemistry, University of California at San Diego

## Casimir Force at a Knife’s Edge

### Noah Graham

^{1}, Alexander Shpunt^{2}, Thorsten Emig^{2, 3, 4}, Sahand Jamal Rahi^{2}, Robert L. Jaffe^{2, 5}, Mehran Kardar^{2}#### Physical Review D

**81**(2010) 061701The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $\theta$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.

- 1. Middlebury College, Middlebury Colleg
- 2. Department of Physics, Massachusetts Institute of Technology
- 3. Institut für Theoretische Physik, Universität zu Köln
- 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 5. Center for Theoretical Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology

**17**)## Casimir Physics: Geometry, Shape and Material

### Thorsten Emig

^{1, 2}#### International Journal of Modern Physics A

**25**, 11 (2010) 2177-2195The properties of fluctuation induced interactions like van der Waals and Casimir-Lifshitz forces are of interest in a plethora of fields ranging from biophysics to nanotechnology. Here we describe a general approach to compute these interactions. It is based on a combination of methods from statistical physics and scattering theory. We showcase how it is exquisitely suited to analyze a variety of previously unexplored phenomena. Examples are given to show how the interplay of geometry and material properties helps to understand and control these forces.

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

**6**)## Casimir potential of a compact object enclosed by a spherical cavity

### Saad Zaheer

^{1}, Sahand Jamal Rahi^{1}, Thorsten Emig^{2, 3}, Robert L. Jaffe^{4}#### Physical Review A: Atomic, Molecular and Optical Physics

**82**(2010) 052507We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.

- 1. Department of Physics, Massachusetts Institute of Technology
- 2. Institut für Theoretische Physik, Universität zu Köln
- 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 4. Center for Theoretical Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology

**9**)## Challenges in experimental data integration within genome-scale metabolic models

### Pierre-Yves Bourguignon

^{1}, Areejit Samal^{2, 3}, François Képès^{4}, Jürgen Jost^{2, 5}, Olivier C. Martin^{3}#### Algorithms for Molecular Biology : AMB

**5**(2010) 20A report of the meeting 'Challenges in experimental data integration within genome-scale metabolic models', Institut Henri Poincaré, Paris, October 10-11 2009, organized by the CNRS-MPG joint program in Systems Biology.

- 1. Genoscope-Centre national de séquençage (GENOSCOPE), CEA : DSV/IG
- 2. Max Planck Institute for Mathematics in the Sciences (MPI-MIS), Max-Planck-Institut
- 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 4. Génopole [Evry], Université d'Evry-Val-d'Essonne
- 5. Santa Fe Institute, Santa Fe Institute

## Chaotic Hamiltonian systems revisited: Survival probability

### V. A. Avetisov

^{1}, S. K. Nechaev^{2, 3}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**81**(2010) 046211We consider the dynamical system described by the area--preserving standard mapping. It is known for this system that $P(t)$, the normalized number of recurrences staying in some given domain of the phase space at time $t$ (so-clled 'survival probability') has the power--law asymptotics, $P(t)\sim t^{-\nu}$. We present new semi--phenomenological arguments which enable us to map the dynamical system near the chaos border onto the effective 'ultrametric diffusion' on the boundary of a tree--like space with hierarchically organized transition rates. In the frameworks of our approach we have estimated the exponent $\nu$ as $\nu=\ln 2/\ln (1+r_g)\approx 1.44$, where $r_g=(\sqrt{5}-1)/2$ is the critical rotation number.

- 1. The Semenov Institute of Chemical Physics, Russian Academy of Sciences
- 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 3. P. N. Lebedev Physical Institute, Russian Academy of Science

## Clustering properties, Jack polynomials and unitary conformal field theories

### Benoit Estienne

^{1}, Nicolas Regnault^{2}, Raoul Santachiara^{3}#### Nuclear Physics B

**824**, 3 (2010) 539Recently, Jack polynomials have been proposed as natural generalizations of Z_k Read-Rezayi states describing non-Abelian fractional quantum Hall systems. These polynomials are conjectured to be related to correlation functions of a class of W-conformal field theories based on the Lie algebra A_{k-1}. These theories can be considered as non-unitary solutions of a more general series of CFTs with Z_k symmetry, the parafermionic theories. Starting from the observation that some parafermionic theories admit unitary solutions as well, we show, by computing the corresponding correlation functions, that these theories provide trial wavefunctions which satisfy the same clustering properties as the non-unitary ones. We show explicitly that, although the wavefunctions constructed by unitary CFTs cannot be expressed as a single Jack polynomial, they still show a fine structure where the mathematical properties of the Jack polynomials play a major role.

- 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
- 2. Laboratoire Pierre Aigrain (LPA), CNRS : UMR8551 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – Ecole Normale Supérieure de Paris - ENS Paris
- 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

## Coherent dynamics of macroscopic electronic order through a symmetry breaking transition

### Yusupov, R., Brazovskii, S., and, al.

#### Nature Physics6 (2010) 681-684

## Coherent dynamics of macroscopic electronic order through a symmetry-breaking transition

### R. Yusupov

^{1}, T. Mertelj^{1}, V. V. Kabanov^{1}, S. Brazovskii^{2}, P. Kusar^{1}, J. -H. Chu^{3}, I. R. Fisher^{3}, D. Mihailovic^{1}#### Nature Physics

**6**(2010) 681-684The temporal evolution of systems undergoing symmetry breaking phase transitions (SBTs) is of great fundamental interest not only in condensed matter physics, but extends from cosmology to brain function and finance \cite{topology,Kibble,Eltsov,Finance}. However, the study of such transitions is often hindered by the fact that they are difficult to repeat, or they occur very rapidly. Here we report for the first time on a high-time-resolution study of the evolution of both bosonic and fermionic excitations through a second order electronic charge-ordering SBT in a condensed matter system. Using a new three-pulse femtosecond spectroscopy technique, we periodically quench our model system into the high-symmetry state, detecting hitherto unrecorded coherent aperiodic undulations of the order parameter (OP), critical slowing down of the collective mode, and evolution of the particle-hole gap appearing through the Peierls-BCS mechanism as the system evolves through the transition. Numerical modeling based on Ginzburg-Landau theory is used to reproduce the observations without free parameters. The close analogy with other Higgs potentials in particle physics\cite{Higgs} gives new insight into hitherto unexplored dynamics of both single particle and collective excitations through a SBT. Of particular interest is the observation of spectro-temporal distortions caused by disturbances of the field arising from spontaneous annihilation of topological defects, similar to those discussed by the Kibble-Zurek cosmological model.

- 1. Department of Complex Matter, Jozef Stefan Institute
- 3. Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University

## Condensation Transition in Polydisperse Hard Rods

### M. R. Evans

^{1}, S. N. Majumdar^{2}, I. Pagonabarraga^{3}, E. Trizac^{2}#### The Journal of Chemical Physics

**132**(2010) 014102We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=\sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles, referred to as $p$-spheres, have a linear size that behaves as $v_i^{1/p}$ and our model thus represents a gas of polydisperse hard rods with variable diameters $v_i^{1/p}$. We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard rod system, under the constraints of fixed $N$ and $V$. Complementary approaches (explicit construction of the steady state distribution on the one hand ; density functional theory on the other hand) completely and consistently specify the behaviour of the system. A real space condensation transition is shown to take place for $p>1$: beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles.

- 1. SUPA and School of Physics, University of Edinburgh
- 3. Departament de Física Fonamental, Universitat de Barcelona, Departament de Física Fonamental, Universitat de Barcelona

## Constraints on stable equilibria with fluctuation-induced forces

### Sahand Jamal Rahi

^{1}, Mehran Kardar^{1}, Thorsten Emig^{2, 3}#### Physical Review Letters

**105**(2010) 070404We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges, and show that any arrangement in space is unstable to small perturbations in position. This extends Earnshaw's theorem for electrostatics by including thermal fluctuations of internal charges. Quantum fluctuations of the electromagnetic field are responsible for Casimir/van der Waals interactions. Neglecting permeabilities, we find that any equilibrium position of items subject to such forces is also 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. Institut für Theoretische Physik, Universität zu Köln

**29**)## Critical interface: twisting spin glasses at $T_c$

### E. Brézin

^{1}, S. Franz^{2}, G. Parisi^{3, 4}#### Physical Review B

**82**(2010) 144427We consider identical copies of spin glasses in finite dimension coupled at the boundaries. This allows to identify the spin glass analogous of twisted boundary conditions in ferromagnetic system and leads to the definition of an interface free-energy that is positively defined and that should scale with a positive power of the system size in the spin glass phase. In this note we study the behavior of the interface at the spin glass critical temperature $T_c$ within mean field theory. We show that the leading scaling of the interface free-energy does not depend on replica symmetry breaking, and can be obtained by simple scaling arguments using a cubic theory for critical spin glasses.

- 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
- 3. Dipartimento di Fisica, “Sapienza” Università di Roma
- 4. INFM-CNR SMC, “Sapienza” Università di Roma, – INFN

## Critical interfaces of the Ashkin-Teller model at the parafermionic point

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

#### Journal of Statistical Mechanics(2010) P07027

Details## Decomposition of spectral density in individual eigenvalue contributions

### O. Bohigas

^{1}, M. P. Pato^{1, 2}#### Journal of Physics A Mathematical and Theoretical

**43**(2010) 365001The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of all eigenvalues, for medium matrix sizes, are described with a good precision by nearly normal distributions.

- 2. Instituto de Fisica, Universidade de São Paulo

**1**)## Dimeric and dipolar ground state orders in colloidal molecular crystals

### Trizac, E., El Shawish, S., Dobnikar, J.

#### Anais da Academia Brasileira de Ciencias82 (2010) 87-94

## Disorder-driven quantum phase transitions in superconductors and magnets

### Lev Ioffe

^{1}, Marc Mezard^{2}#### Physical Review Letters

**105**(2010) 037001We develop an analytical theory, based on the quantum cavity method, describing the quantum phase transitions in low-temperature, strongly disordered ferromagnets and superconductors. At variance with the usual quantum critical points, we find a phase diagram with two critical points separating three phases. When the disorder increases, the systems goes from the ordered phase to an intermediate disordered phase characterized by activated transport and then to a second disordered phase where no transport is possible. Both the ordered and disordered phases exhibit strong inhomogeneity of their basic properties typical of glassy physics.

- 1. Department of Physics and Astronomy, Center for Materials Theory, Rutgers University

## Distribution of essential interactions in model gene regulatory networks under mutation-selection balance

### Z. Burda

^{1}, A. Krzywicki^{2}, O. C. Martin^{3, 4}, M. Zagorski^{1}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**82**(2010) 011908Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What mechanisms might be responsible for these degree distributions? Starting with an accepted framework of the binding of transcription factors to DNA, we consider a simple model of gene regulatory dynamics. There, we show that selection for a target expression pattern leads to the emergence of minimum connectivities compatible with the selective constraint. As a consequence, these gene networks have low in-degree, and 'functionality' is parsimonious, i.e. is concentrated on a sparse number of interactions as measured for instance by their essentiality. Furthermore, we find that mutations of the transcription factors drive the networks to have broad out-degrees. Finally, these classes of models are evolvable, i.e. significantly different genotypes can emerge gradually under mutation-selection balance.

- 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 – Institut National Agronomique Paris-Grignon

## Domain walls at the spin density wave enpoint of the organic superconductor (TMTSF)_{2}PF_{6} under pressure

### Kang, W., Salameh, B., Auban Senzier, P., Jerome, D., Pasquier, C.R., Brazovskii, S.

#### Physical Review B81 (2010) 100509

Details## Effect of boundaries on the spectrum of a one-dimensional random mass Dirac Hamiltonian

### Christophe Texier

^{1, 2}, Christian Hagendorf^{3}#### Journal of Physics A General Physics

**43**(2010) 025002The average density of states (DoS) of the one-dimensional Dirac Hamiltonian with a random mass on a finite interval [0,L] is derived. Our method relies on the eigenvalues distributions (extreme value statistics problem) which are explicitly obtained. The well-known Dyson singularity \sim-L/|epsilon|ln^3|\epsilon| is recovered above the crossover energy epsilon_c\sim exp-sqrt{L}. Below epsilon_c we find a log-normal suppression of the average DoS \sim 1/(|epsilon|sqrt(L))exp(-(ln^2|epsilon|)/L).

- 2. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
- 3. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

**3**)## Electron-quasihole duality and second-order differential equation for Read-Rezayi and Jack wave functions

### Estienne, B., Bernevig, A., Santachiara, R.

#### Physical Review B82 (2010) 205307

Details## Emergence of rigidity at the structural glass transition: a first principle computation

### Hajime Yoshino

^{1}, Marc Mezard^{2}#### Physical Review Letters

**105**(2010) 015504We compute the shear modulus of structural glasses from a first principle approach based on the cloned liquid theory. We find that the intra-state shear-modulus, which corresponds to the plateau modulus measured in linear visco-elastic measurements, strongly depends on temperature and vanishes continuously when the temperature is increased beyond the glass temperature.

- 1. Department of Earth and Space Science, Osaka University

## Experimental test of a trace formula for two-dimensional dielectric resonators

### S. Bittner

^{1}, E. Bogomolny^{2}, B. Dietz^{3}, M. Miski-Oglu^{3}, P. Oria Iriarte^{1}, A. Richter^{1, 4}, F. SchÄfer^{5}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**81**(2010) 066215Resonance spectra of two-dimensional dielectric microwave resonators of circular and square shapes have been measured. The deduced length spectra of periodic orbits were analyzed and a trace formula for dielectric resonators recently proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)] was tested. The observed deviations between the experimental length spectra and the predictions of the trace formula are attributed to a large number of missing resonances in the measured spectra. We show that by taking into account the systematics of observed and missing resonances the experimental length spectra are fully understood. In particular, a connection between the most long-lived resonances and certain periodic orbits is established experimentally.

- 1. Institut für Kernphysik, Technische Universität Darmstadt
- 3. Institut für Kernphysik, Technische Universität Darmstadt
- 4. ECT, Villa Tombosi, Villa Tombosi
- 5. LENS, University of Fiorentino

**7**)## Finite size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model

### M. Colomé-Tatché

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

**81**(2010) 013611We study finite size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two type of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due to gapless excitations which behaves as $1/N_a$, where $N_a$ is the number of lattice sites, we obtain corrections related to the existence of gapped excitations. First of all, there is an exponential correction which in the weakly interacting regime ($|U|\ll t$) behaves as $\sim \exp (-N_a \Delta_{\infty}/4 t)$ in the extreme limit of $N_a \Delta_{\infty} /t \gg 1$, where $t$ is the hopping amplitude, $U$ is the on-site energy, and $\Delta_{\infty}$ is the gap in the thermodynamic limit. Second, in a finite size system a spin-flip producing unpaired fermions leads to the appearance of solitons with non-zero momenta, which provides an extra (non-exponential) contribution $\delta$. For moderate but still large values of $N_a\Delta_{\infty} /t$, these corrections significantly increase and may become comparable with the $1/N_a$ conformal correction. Moreover, in the case of weak interactions where $\Delta_{\infty}\ll t$, the exponential correction exceeds higher order power law corrections in a wide range of parameters, namely for $N_a\lesssim (8t/\Delta_{\infty})\ln(4t/|U|)$, and so does $\delta$ even in a wider range of $N_a$. For sufficiently small number of particles, which can be of the order of thousands in the weakly interacting regime, the gap is fully dominated by finite size effects.

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

## Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model

### Guillaume Roux

^{1}#### Physical Review A: Atomic, Molecular and Optical Physics

**81**(2010) 053604We investigate finite size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy-scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground-states. Both criteria can be computed using ground-state techniques that work for larger system sizes than full spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap which frequency is quenched, and the one-dimensional Bose-Hubbard model, that is known to be non-integrable and for which recent studies have uncovered remarkable non-equilibrium behaviors. The diagonal weights of the time-averaged density-matrix are computed and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the ``thermalized'' regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite size effects that render difficult a thorough comparison with statistical ensembles. In addition, we show that the non-thermalized regime, emerging on finite size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the non-interacting limit to the atomic limit.

**40**)## Finite temperature phase transition for disordered weakly interacting bosons in one dimension

### I. L. Aleiner

^{1}, B. L. Altshuler^{2}, G. V. Shlyapnikov^{3, 4}#### Nature Physics

**6**(2010) 900-904It is commonly accepted that there are no phase transitions in one-dimensional (1D) systems at a finite temperature, because long-range correlations are destroyed by thermal fluctuations. Here we demonstrate that the 1D gas of short-range interacting bosons in the presence of disorder can undergo a finite temperature phase transition between two distinct states: fluid and insulator. None of these states has long-range spatial correlations, but this is a true albeit non-conventional phase transition because transport properties are singular at the transition point. In the fluid phase the mass transport is possible, whereas in the insulator phase it is completely blocked even at finite temperatures. We thus reveal how the interaction between disordered bosons influences their Anderson localization. This key question, first raised for electrons in solids, is now crucial for the studies of atomic bosons where recent experiments have demonstrated Anderson localization in expanding very dilute quasi-1D clouds.

- 1. Physics Department, Columbia University
- 2. Physics Dept., Columbia University, new York
- 4. Van der Waals-Zeeman Institute, University of Amsterdam

## Fractal superconductivity near localization threshold

### M. V. Feigel'man

^{1, 2}, L. B. Ioffe^{1, 3, 4}, V. E. Kravtsov^{1, 5}, E. Cuevas^{6}#### Annals of Physics / Ann Phys (New York); Annals of Physics (New York); Ann Phys (U S A ); Ann Phys (Leipzig)

**325**, 7 (2010) 1390-1478We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk 'poor conductors' in which Fermi energy $E_F$ is located in the region of localized states not so far from the Anderson mobility edge $E_c$. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model. Our theoretical analysis is based on the analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems. We identify three distinct phases: 'critical' superconductive state formed at $E_F=E_c$, superconducting state with a strong pseudogap, realized due to pairing of weakly localized electrons and insulating state realized at $E_F$ still deeper inside localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gaped state is the presence of two independent energy scales: superconducting gap $\Delta$, that is due to many-body correlations and a new 'pseudogap' energy scale $\Delta_P$ which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive $T_c$. Two gap nature of the 'pseudo-gaped superconductor' is shown to lead to a number of unusual physical properties.

- 1. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
- 2. Moscow Institute of Physics and Technology (MIPT), Moscow Institute of Physics and Technology
- 4. Department of Physics and Astronomy, University of California, Riverside
- 5. The Abdus Salam International Centre for Theoretical Physics, ICTP Trieste
- 6. Izaña Atmospheric Research Center, Izaña Atmospheric Research Center

## Fractional quantum Hall states with negative flux: edge modes in some Abelian and non-Abelian cases

### M. V. Milovanović

^{1}, Th. Jolicoeur^{2}#### International Journal of Modern Physics B

**24**(2010) 549We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general quantum Hall states have many edge states. Here we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve in all cases explicit derivative operators diminishing the angular momentum of the system.

- 1. Institute of Physics, Institute of Physics

## Free-energy distribution of the directed polymer at high temperature

### Pasquale Calabrese

^{1}, Pierre Le Doussal^{2}, Alberto Rosso^{3}#### Europhysics Letters (EPL)

**90**(2010) 20002We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is described, upon scaling 'time' $t \sim T^5/\kappa$ and space $x = T^3/\kappa$ (with $\kappa=T$ for the discrete model) by a continuum model with $\delta$-function disorder correlation. Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function. The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics. We then obtain the exact expression at any time for the generating function of the free energy distribution, in terms of a Fredholm determinant. At large time we find that it crosses over to the Tracy Widom distribution (TW) which describes the fixed $T$ infinite $t$ limit. The exact free energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.

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

## Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities

### Yan V Fyodorov

^{1}, Pierre Le Doussal^{2}, Alberto Rosso^{3}#### Europhysics Letters (EPL)

**90**(2010) 60004We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities

- 1. School of Mathematical Sciences, University of Nottingham
- 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

## Genotype networks in metabolic reaction spaces

### Areejit Samal

^{1, 2, 3}, Joao F. Matias Rodrigues^{4}, Jürgen Jost^{1, 5}, Olivier C. Martin^{2, 6}, Andreas Wagner^{4, 5, 7, 8}#### BMC Biology

**4**(2010) 30Background: A metabolic genotype comprises all chemical reactions an organism can catalyze via enzymes encoded in its genome. A genotype is viable in a given environment if it is capable of producing all biomass components the organism needs to survive and reproduce. Previous work has focused on the properties of individual genotypes while little is known about how genome-scale metabolic networks with a given function can vary in their reaction content. Results: We here characterize spaces of such genotypes. Specifically, we study metabolic genotypes whose phenotype is viability in minimal chemical environments that differ in their sole carbon sources. We show that regardless of the number of reactions in a metabolic genotype, the genotypes of a given phenotype typically form vast, connected, and unstructured sets -- genotype networks -- that nearly span the whole of genotype space. The robustness of metabolic phenotypes to random reaction removal in such spaces has a narrow distribution with a high mean. Different carbon sources differ in the number of metabolic genotypes in their genotype network; this number decreases as a genotype is required to be viable on increasing numbers of carbon sources, but much less than if metabolic reactions were used independently across different chemical environments. Conclusions: Our work shows that phenotype-preserving genotype networks have generic organizational properties and that these properties are insensitive to the number of reactions in metabolic genotypes.

- 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
- 4. Department of Biochemistry, University of Zurich
- 5. Santa Fe Institute, Santa Fe Institute
- 6. Laboratoire de Génétique Végétale du Moulon, Université Paris XI - Paris Sud
- 7. Swiss Institute of Bioinformatics (SIB), Swiss Institute of Bioinformatics
- 8. Department of Biology, University of New Mexico

## Graphene n-p junction in a strong magnetic field: a semiclassical study

### Pierre Carmier

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

**81**(2010) 241406We provide a semiclassical description of the electronic transport through graphene n-p junctions in the quantum Hall regime. A semiclassical approximation for the conductance is derived in terms of the various snake-like trajectories at the interface of the junction. For a symmetric (ambipolar) configuration, the general result can be recovered by means of a simple scattering approach, providing a very transparent qualitative description of the problem under study. Consequences of our findings for the understanding of recent experiments are discussed.

- 2. Instituto de Fisica, Universidade Federal Fluminense

**6**)## Haldane charge conjecture in one-dimensional multicomponent fermionic cold atoms

### H. Nonne

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

**81**(2010) 020408 RA Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and gapped phases depending on the parity of N for attractive interactions at half-filling. In particular, the analogue of the Haldane phase of the spin-1 Heisenberg chain is stabilized for N = 2 with non-local string charge correlation, and pseudo-spin 1/2 edge states. At the heart of this even-odd behavior is the existence of spin-singlet pseudo-spin N/2 operator which governs the low-energy properties of the model for attractive interactions and give rise to the Haldane physics.

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

**12**)## Hearing shapes of drums – mathematical and physical aspects of isospectrality

### O. Giraud

^{1}, K. Thas^{2}#### Reviews of Modern Physics

**82**(2010) 2213-2255In a celebrated paper ''Can one hear the shape of a drum?'' M. Kac [Amer. Math. Monthly 73, 1 (1966)] asked his famous question about the existence of nonisometric billiards having the same spectrum of the Laplacian. This question was eventually answered positively in 1992 by the construction of noncongruent planar isospectral pairs. This review highlights mathematical and physical aspects of isospectrality.

- 2. Department of Pure Mathematics and Computer Algebra, Ghent University

**6**)## Hitting probability for anomalous diffusion processes

### Satya N. Majumdar

^{1}, Alberto Rosso^{1}, Andrea Zoia^{2}#### Physical Review Letters

**104**(2010) 020602We present the universal features of the hitting probability $Q(x,L)$, the probability that a generic stochastic process starting at $x$ and evolving in a box $[0,L]$ hits the upper boundary $L$ before hitting the lower boundary at 0. For a generic self-affine process (describing, for instance, the polymer translocation through a nanopore) we show that $Q(x,L)=Q(x/L)$ and the scaling function $Q(z)\sim z^\phi$ as $z\to 0$ with $\phi=\theta/H$ where $H$ and $\theta$ are respectively the Hurst exponent and the persistence exponent of the process. This result is verified in several exact calculations including when the process represents the position of a particle diffusing in a disordered potential. We also provide numerical supports for our analytical results.

- 2. CEA/Saclay, CEA

**10**)## Interlayer superfluidity in bilayer systems of fermionic polar molecules

### A. Pikovski

^{1}, M. Klawunn^{1, 2}, G. V. Shlyapnikov^{3, 4}, L. M.N.B.F. Santos^{1}#### Physical Review Letters

**105**(2010) 215302We consider fermionic polar molecules in a bilayer geometry where they are oriented perpendicularly to the layers, which permits both low inelastic losses and superfluid pairing. The dipole-dipole interaction between molecules of different layers leads to the emergence of interlayer superfluids. The superfluid regimes range from BCS-like fermionic superfluidity with a high $T_c$ to Bose-Einstein (quasi-)condensation of interlayer dimers, thus exhibiting a peculiar BCS-BEC crossover. We show that one can cover the entire crossover regime under current experimental conditions.

- 1. Institut fur Theoretische Physik, Leibniz Universität Hannover
- 2. INO-CNR BEC, Universita di Trento
- 4. Van der Waals-Zeeman Institute, University of Amsterdam

**43**)## Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction

### Jérôme Roccia

^{1}, Patricio Leboeuf^{2}#### Physical Review C

**81**(2010) 044301We investigate the many-body level density of gas of non-interacting fermions. We determine its behavior as a function of the temperature and the number of particles. As the temperature increases, and beyond the usual Sommerfeld expansion that describes the degenerate gas behavior, corrections due to a finite number of particles lead to Gumbel-like contributions. We discuss connections with the partition problem in number theory, extreme value statistics as well as differences with respect to the Bose gas.

- 1. Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), Université de Strasbourg – CNRS : UMR7504

**1**)## Localization by bichromatic potentials versus Anderson localization

### Mathias Albert

^{1}, Patricio Leboeuf^{1}#### Physical Review A: Atomic, Molecular and Optical Physics

**81**(2010) 013614The one-dimensional propagation of waves in a bichromatic potential may be modeled by the Aubry-André Hamiltonian. The latter presents a delocalization-localization transition, which has been observed in recent experiments using ultracold atoms or light. It is shown here that, in contrast to Anderson localization, this transition has a classical origin, namely the localization mechanism is not due to a quantum suppression of a classically allowed transport process. Explicit comparisons with the Anderson model, as well as with experiments, are done.

**15**)## Luttinger liquid of trimers in Fermi gases with unequal masses

### Giuliano Orso

^{1}, Evgeni Burovski^{1}, Thierry Jolicoeur^{1}#### Physical Review Letters, 104 (2010) 065301

We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. Starting from the asymmetric Hubbard model, we show that three-body bound states - ``trimers'' - exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite commensurate densities $n_\uparrow=n_\downarrow/2$ an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid ordering. The boundaries of this exotic phase are given.

## Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers

### Satya N. Majumdar

^{1}, Alan J. Bray^{2}#### Journal of Statistical Mechanics (2010) P08023

We consider three independent Brownian walkers moving on a line. The process terminates when the left-most walker (the `Leader') meets either of the other two walkers. For arbitrary values of the diffusion constants D_1 (the Leader), D_2 and D_3 of the three walkers, we compute the probability distribution P(m|y_2,y_3) of the maximum distance m between the Leader and the current right-most particle (the `Laggard') during the process, where y_2 and y_3 are the initial distances between the leader and the other two walkers. The result has, for large m, the form P(m|y_2,y_3) \sim A(y_2,y_3) m^{-\delta}, where \delta = (2\pi-\theta)/(\pi-\theta) and \theta = cos^{-1}(D_1/\sqrt{(D_1+D_2)(D_1+D_3)}. The amplitude A(y_2,y_3) is also determined exactly.

- 2. School of Physics and Astronomy, University of Manchester

## Maximum of N Independent Brownian Walkers till the First Exit From the Half Space

### P. L. Krapivsky

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

**43**(2010) 315001We consider the one-dimensional target search process that involves an immobile target located at the origin and $N$ searchers performing independent Brownian motions starting at the initial positions $\vec x = (x_1,x_2,..., x_N)$ all on the positive half space. The process stops when the target is first found by one of the searchers. We compute the probability distribution of the maximum distance $m$ visited by the searchers till the stopping time and show that it has a power law tail: $P_N(m|\vec x)\sim B_N (x_1x_2... x_N)/m^{N+1}$ for large $m$. Thus all moments of $m$ up to the order $(N-1)$ are finite, while the higher moments diverge. The prefactor $B_N$ increases with $N$ faster than exponentially. Our solution gives the exit probability of a set of $N$ particles from a box $[0,L]$ through the left boundary. Incidentally, it also provides an exact solution of the Laplace's equation in an $N$-dimensional hypercube with some prescribed boundary conditions. The analytical results are in excellent agreement with Monte Carlo simulations.

- 1. Center for Polymer Studies (CPS), Boston University

**5**)## Microwave-induced Fano-Feshbach resonances

### Papoular, D.J., Shlyapnikov, G.V., Dalibard, J.

#### Physical Review A81 (2010) 041603

## Moore-Read fractional quantum Hall wave functions and SU(2) quiver gauge theories

### Santachiara, R., Tanzini, A.

#### Physical Review D82 (2010) 126006

Details## Multifractal wave functions of simple quantum maps

### John Martin

^{1}, Ignacio Garcia-Mata^{1}, Olivier Giraud^{1, 2}, Bertrand Georgeot^{1}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**82**(2010) 046206We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting method and wavelet method). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects.

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

**4**)## Multiqubit symmetric states with high geometric entanglement

### J. Martin

^{1}, Olivier Giraud^{2, 3}, P. A. Braun^{4, 5}, Daniel Braun^{2}, T. Bastin^{6}#### Physical review A: Atomic, Molecular and Optical Physics

**81**(2010) 062347We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement behaves asymptotically for large N. We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously. We also derive an upper bound for the geometric measure of entanglement of symmetric states. The connection with the quantumness of a state is discussed.

- 1. Institut de Physique Nucléaire, Atomique et de Spectrométrie, Université de Liège
- 2. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
- 4. Fachbereich Physik, Univestität Duisbourg-Essen
- 5. Institute of Physik, Saint Petersbourg University
- 6. Institut de Physique Nucléaire, Atomique et de Spectrométrie, Université de Liège

**22**)## On the motif distribution in random block-hierarchical networks

### V. A. Avetisov

^{1}, S. K. Nechaev^{2, 3, 4}, A. B. Shkarin^{5}#### Physica A: Statistical Mechanics and its Applications

**389**, 24 (2010) 5895-5902The distribution of motifs in random hierarchical networks defined by nonsymmetric random block--hierarchical adjacency matrices, is constructed for the first time. According to the classification of U. Alon et al of network superfamilies by their motifs distributions, our artificial directed random hierarchical networks falls into the superfamily of natural networks to which the class of neuron networks belongs. This is the first example of ``handmade'' networks with the motifs distribution as in a special class of natural networks of essential biological importance.

- 1. The Semenov Institute of Chemical Physics, Russian Academy of Sciences
- 3. P. N. Lebedev Physical Institute, Russian Academy of Science
- 4. JV Poncelet Laboratory, Independant University
- 5. Moscow Institute of Physics and Technology (MIPT), Moscow Institute of Physics and Technology

## Pair Density Waves in coupled doped two-leg Ladders

### Javier Almeida

^{1}, Guillaume Roux^{2}, Didier Poilblanc^{1}#### Physical Review B

**82**(2010) 041102Motivated by Resonant X-ray scattering experiments in cuprate ladder materials showing charge order modulation of period $\lambda=3$ and 5 at specific hole densities, we investigate models involving the electronic t-J ladders and bosonic chains coupled via screened Coulomb repulsion. Extensive density matrix renormalization group calculations applied to the ladders/chains supplemented by a self-consistent mean-field treatment of the inter-ladder/chain coupling provide quantitative estimates of the charge order for $\lambda=3,4$ and 5. As previously proposed, such patterns correspond to the emergence of pair density waves which stem from the strong electronic correlations. We comment on the existence of a $\lambda=4$ modulation not seen so far in experiment.

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

**3**)## Physical theory of excitons in conducting polymers

### Brazovskii, S., Kirova, N.

#### Chemical Society Review39 (2010) 2453-2465

## Probability distributions of Linear Statistics in Chaotic Cavities and associated phase transitions

### Pierpaolo Vivo

^{1}, Satya N. Majumdar^{2}, Oriol Bohigas^{2}#### Physical Review B

**81**(2010) 104202We establish large deviation formulas for linear statistics on the $N$ transmission eigenvalues $\{T_i\}$ of a chaotic cavity, in the framework of Random Matrix Theory. Given any linear statistics of interest $A=\sum_{i=1}^N a(T_i)$, the probability distribution $\mathcal{P}_A(A,N)$ of $A$ generically satisfies the large deviation formula $\lim_{N\to\infty}[-2\log\mathcal{P}_A(Nx,N)/\beta N^2]=\Psi_A(x)$, where $\Psi_A(x)$ is a rate function that we compute explicitly in many cases (conductance, shot noise, moments) and $\beta$ corresponds to different symmetry classes. Using these large deviation expressions, it is possible to recover easily known results and to produce new formulas, such as a closed form expression for $v(n)=\lim_{N\to\infty}\mathrm{var}(\mathcal{T}_n)$ (where $\mathcal{T}_n=\sum_{i}T_i^n$) for arbitrary integer $n$. The universal limit $v^\star=\lim_{n\to\infty} v(n)=1/2\pi\beta$ is also computed exactly. The distributions display a central Gaussian region flanked on both sides by non-Gaussian tails. At the junction of the two regimes, weakly non-analytical points appear, a direct consequence of phase transitions in an associated Coulomb gas problem. Numerical checks are also provided, which are in full agreement with our asymptotic results in both real and Laplace space even for moderately small $N$. Part of the results have been announced in [P. Vivo, S.N. Majumdar and O. Bohigas, {\it Phys. Rev. Lett.} {\bf 101}, 216809 (2008)].

- 1. The Abdus Salam International Centre for Theoretical Physics, ICTP Trieste

## Products of random matrices and generalised quantum point scatterers

### Alain Comtet

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

**140**(2010) 427-466To every product of $2\times2$ matrices, there corresponds a one-dimensional Schr\'{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and their positions random. We exhibit a simple one-dimensional quantum model corresponding to the most general product of matrices in $\text{SL}(2, {\mathbb R})$. We use this correspondence to find new examples of products of random matrices for which the invariant measure can be expressed in simple analytical terms.

- 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

**2**)## Quantifying Quantumness and the Quest for Queens of Quantum

### Olivier Giraud

^{1, 2}, Petr A. Braun^{3, 4}, Daniel Braun^{1}#### New Journal of Physics

**12**(2010) 063005We introduce a measure of ''quantumness'' for any quantum state in a finite dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter are defined as states that can be written as a convex sum of projectors onto coherent states. We derive general properties of this measure of non-classicality, and use it to identify for a given dimension of Hilbert space what are the 'Queen of Quantum' states, i.e. the most non-classical quantum states. In three dimensions we obtain the Queen of Quantum state analytically and show that it is unique up to rotations. In up to 11-dimensional Hilbert spaces, we find the Queen of Quantum states numerically, and show that in terms of their Majorana representation they are highly symmetric bodies, which for dimensions 5 and 7 correspond to Platonic bodies.

- 1. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
- 3. Fachbereich Physik, Univestität Duisbourg-Essen
- 4. Institute of Physik, Saint Petersbourg University

## Quantifying Slow Evolutionary Dynamics in RNA Fitness Landscapes

### P. Sulc

^{1}, A. Wagner^{2, 3}, O. C. Martin^{1, 4}#### Journal of Bioinformatics and Computational Biology

**8**(2010) 1027-1040We re-examine the evolutionary dynamics of RNA secondary structures under directional selection towards an optimum RNA structure. We find that the punctuated equilibria lead to a very slow approach to the optimum, following on average an inverse power of the evolutionary time. In addition, our study of the trajectories shows that the out-of-equilibrium effects due to the evolutionary process are very weak. In particular, the distribution of genotypes is close to that arising during equilibrium stabilizing selection. As a consequence, the evolutionary dynamics leave almost no measurable out-of-equilibrium trace, only the transition genotypes (close to the border between different periods of stasis) have atypical mutational properties.

- 2. Department of Biochemistry, University of Zurich
- 3. Santa Fe Institute, Santa Fe Institute
- 4. Génétique Végétale (GV), CNRS : UMR8120 – Institut national de la recherche agronomique (INRA) : UMR0320 – Université Paris XI - Paris Sud – AgroParisTech

## Quantum algorithm for exact Monte Carlo sampling

### Nicolas Destainville

^{1}, Bertrand Georgeot^{1}, Olivier Giraud^{1, 2}#### Physical Review Letters

**104**(2010) 250502We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact Monte Carlo sampling methods, and yields a polynomial gain compared to classical procedures.

## Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models

### Roya Zandi

^{1}, Thorsten Emig^{2, 3}, Umar Mohideen^{1}#### Physical Review B

**81**(2010) 195423We calculate the Casimir interaction between a sphere and a plate, both described by the plasma model, the Drude model, or generalizations of the two models. We compare the results at both zero and finite temperatures. At asymptotically large separations we obtain analytical results for the interaction that reveal a non-universal, i.e., material dependent interaction for the plasma model. The latter result contains the asymptotic interaction for Drude metals and perfect reflectors as different but universal limiting cases. This observation is related to the screening of a static magnetic field by a London superconductor. For small separations we find corrections to the proximity force approximation (PFA) that support correlations between geometry and material properties that are not captured by the Lifshitz theory. Our results at finite temperatures reveal for Drude metals a non-monotonic temperature dependence of the Casimir free energy and a negative entropy over a sizeable range of separations.

- 1. Department of Physics and Astronomy, University of California, Riverside
- 2. Institut für Theoretische Physik, Universität zu Köln

## Random Convex Hulls and Extreme Value Statistics

### Satya N. Majumdar

^{1}, Alain Comtet^{1}, Julien Randon-Furling^{2}#### Journal of Statistical Physics

**138**, 6 (2010) 955-1009In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].

- 2. Saarland University, Saarland University

**8**)## Renormalization group computation of the critical exponents of hierarchical spin glasses

### Michele Castellana

^{1, 2}, Giorgio Parisi^{3}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**82**, 4 (2010) 040105The infrared behaviour of a non-mean field spin-glass system is analysed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the epsilon-expansion technique with two independent methods. Both methods yield the same result confirming that the infrared behaviour of the theory if well-defined and the underlying ideas of the Renormalization Group hold also in such non-mean field disordered model. By pushing such calculation to high orders in epsilon, a consistent and predictive non-mean field theory for such disordered system could be established.

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

## Reply to ‘Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined’ »

### Guillaume Roux

^{1}#### Physical Review A: Atomic, Molecular and Optical Physics

**82**(2010) 037602In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy distribution after a quench is not related to standard statistical ensembles and cannot explain thermalization. The latter is proposed to stem from what he calls the eigenstate thermalization hypothesis and which boils down to the fact that simple observables are expected to be smooth functions of the energy. In this Reply, we show that there is no contradiction or confusion between the observations and discussions of Roux and the expected thermalization scenario discussed by Rigol. In addition, we emphasize a few other important aspects, in particular the definition of temperature and the equivalence of ensemble, which are much more difficult to show numerically even though we believe they are essential to the discussion of thermalization. These remarks could be of interest to people interested in the interpretation of the data obtained on finite-size systems.

**1**)## Rheological properties for inelastic Maxwell mixtures under shear flow

### Vicente Garzo

^{1}, Emmanuel Trizac^{2}#### Journal of Non-Newtonian Fluid Mechanics

**165**(2010) 932-940The Boltzmann equation for inelastic Maxwell models is considered to determine the rheological properties in a granular binary mixture in the simple shear flow state. The transport coefficients (shear viscosity and viscometric functions) are {\em exactly} evaluated in terms of the coefficients of restitution, the (reduced) shear rate and the parameters of the mixture (particle masses, diameters and concentration). The results show that in general, for a given value of the coefficients of restitution, the above transport properties decrease with increasing shear rate.

- 1. Departamento de Fisica, Universidad de Extremadura
- 2. LPTMS, University Paris Sud

## Scattering on two Aharonov-Bohm vortices with opposite fluxes

### E. Bogomolny

^{1}, S. Mashkevich^{2, 3}, S. Ouvry^{1}#### Journal of Physics A Mathematical and Theoretical

**43**(2010) 354029The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two vortices. These conditions result in an infinite system of equations for scattering amplitudes between incoming and outgoing partial waves, which can be solved numerically. The main focus of the paper is the analytic determination of the scattering amplitude in two limits, the small flux limit and the limit of small vortex separation. In the latter limit the dominant contribution comes from the S-wave amplitude. Calculating it, however, still requires solving an infinite system of equations, which is achieved by the Riemann-Hilbert method. The results agree well with the numerical calculations.

- 2. Schrödinger, Schrodinger
- 3. Bogolyubov Institute for Theoretical Physics, Bogolyobov Institute for Theoretical Physics

## Spatial and topological organization of DNA chains induced by gene co-localization

### Ivan Junier

^{1, 2}, Olivier C. Martin^{3, 4}, François Képès^{5}#### PLoS Computational Biology

**6**, 2 (2010) 1000678Transcriptional activity has been shown to relate to the organization of chromosomes in the eukaryotic nucleus and in the bacterial nucleoid. In particular, highly transcribed genes, RNA polymerases and transcription factors gather into discrete spatial foci called transcription factories. However, the mechanisms underlying the formation of these foci and the resulting topological order of the chromosome remain to be elucidated. Here we consider a thermodynamic framework based on a worm-like chain model of chromosomes where sparse designated sites along the DNA are able to interact whenever they are spatially close-by. This is motivated by recurrent evidence that there exists physical interactions between genes that operate together. Three important results come out of this simple framework. First, the resulting formation of transcription foci can be viewed as a micro-phase separation of the interacting sites from the rest of the DNA. In this respect, a thermodynamic analysis suggests transcription factors to be appropriate candidates for mediating the physical interactions between genes. Next, numerical simulations of the polymer reveal a rich variety of phases that are associated with different topological orderings, each providing a way to increase the local concentrations of the interacting sites. Finally, the numerical results show that both one-dimensional clustering and periodic location of the binding sites along the DNA, which have been observed in several organisms, make the spatial co-localization of multiple families of genes particularly efficient.

- 1. Epigenomics Project, University of Evry
- 2. Institut des Systèmes Complexes - Paris Ile-de-France (ISC-PIF), CNRS : UMR7656 – Institut Curie – Université Paris XI - Paris Sud – Université Paris I - Panthéon Sorbonne – Université Paris VI - Pierre et Marie Curie – École normale supérieure de Cachan - ENS Cachan – Ecole Normale Supérieure de Paris - ENS Paris – Polytechnique - X
- 4. Station de Génétique Végétale, CNRS : UMR320 – Institut national de la recherche agronomique (INRA)
- 5. Génopole [Evry], Université d'Evry-Val-d'Essonne

## Spectral properties of the Google matrix of the World Wide Web and other directed networks

### Bertrand Georgeot

^{1}, Olivier Giraud^{1, 2}, Dima L. Shepelyansky^{1}#### Physical Review E

**81**(2010) 056109We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter $\alpha$ equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks. We also determine specific properties of eigenstates of the Google matrix, including the PageRank. The fidelity of the PageRank is proposed as a new characterization of its stability.

**15**)## Statistical properties of the spectrum the extended Bose-Hubbard model

### Corinna Kollath

^{1}, Guillaume Roux^{2}, Giulio Biroli^{3}, Andreas Laeuchli^{4}#### Journal of Statistical Mechanics (2010) P08011

Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the ratio of adjacent level spacings, useful at large interaction, to distinguish between chaotic and non-chaotic regimes. After revisiting the bare Bose-Hubbard model, we study the effect of two different perturbations: next-nearest neighbor hopping and nearest-neighbor interaction. The system size dependence is investigated together with the effect of the proximity to integrable points or lines. Lastly, we discuss the consequences of a cutoff in the number of onsite bosons onto the level statistics.

- 1. Centre de Physique Théorique (CPHT), CNRS : UMR7644 – Polytechnique - X
- 3. Institut de Physique Théorique (ex SPhT) (IPHT), CNRS : URA2306 – CEA : DSM/IPHT
- 4. Max Planck Institut für Physic komplexer systeme, Max Planck Institut

**6**)## STDP-driven networks and the \emph{C. elegans} neuronal network

### Quansheng Ren

^{1}, Kiran M. Kolwankar^{1, 2}, Areejit Samal^{1, 3}, Jürgen Jost^{1, 4}#### Physica A: Statistical Mechanics and its Applications

**389**, 18 (2010) 3900-3914We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of \emph{C. elegans} and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.

- 1. Max Planck Institute for Mathematics in the Sciences (MPI-MIS), Max-Planck-Institut
- 2. Department of Physcis Ramniranjan Jhunjhunwala College, Ramniranjan Jhunjhunwala College
- 4. Santa Fe Institute, Santa Fe Institute

## Stochastic qualifier of gel and glass transitions in laponite suspensions

### Shayeganfar, F., Jabbari-Farouji, S., Movahed, M.S., Jafari, G.R., Tabar, M.R.R.

#### Physical Review E81 (2010) 061404

## Superconductor-Insulator transition and energy localization

### M. V. Feigel'man

^{1, 2}, L. B. Ioffe^{1, 3, 4}, M. Mézard^{3}#### Physical Review B

**82**(2010) 184534We develop an analytical theory for generic disorder-driven quantum phase transitions. We apply this formalism to the superconductor-insulator transition and we briefly discuss the applications to the order-disorder transition in quantum magnets. The effective spin-1/2 models for these transitions are solved in the cavity approximation which becomes exact on a Bethe lattice with large branching number K >> 1 and weak dimensionless coupling g << 1. The characteristic features of the low temperature phase is a large self-formed inhomogeneity of the order-parameter distribution near the critical point K_{c}(g) where the critical temperature T_{c} of the ordering transition vanishes. Near the quantum critical point, the typical value of the order parameter vanishes exponentially, B_{0}\propto e^{-C/(K-K_{c}(g))}. In the disordered regime, realized at K

- 1. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
- 2. Moscow Institute of Physics and Technology (MIPT), Moscow Institute of Physics and Technology
- 4. Department of Physics and Astronomy, University of California, Riverside

## Superfluid Motion of Light

### Patricio Leboeuf

^{1}, Simon Moulieras^{1}#### Physical Review Letters

**105**(2010) 163904Superfluidity, the ability of a fluid to move without dissipation, is one of the most spectacular manifestations of the quantum nature of matter. We explore here the possibility of superfluid motion of light. Controlling the speed of a light packet with respect to a defect, we demonstrate the presence of superfluidity and, above a critical velocity, its breakdown through the onset of a dissipative phase. We describe a possible experimental realization based on the transverse motion through an array of waveguides. These results open new perspectives in transport optimization.

**5**)## Suppression of the magneto resistance in high electric fields of polyacetylene nanofibers

### Choi, A., Brazovskii, S., and, al.

#### Synthetic Metal160 (2010) 1349-1353

## Surface Charge Density Wave Transition in NbSe$_3$

### Christophe Brun

^{1}, Zhao-Zhong Wang^{1}, Pierre Monceau^{2}, Serguei Brazovskii^{3}#### Physical Review Letters

**104**(2010) 256403The two charge-density wave (CDW) transitions in NbSe$_3$ %at wave numbers at $\bm{q_1}$ and $\bm{q_2}$, occurring at the surface were investigated by scanning tunneling microscopy (STM) on \emph{in situ} cleaved $(\bm{b},\bm{c})$ plane. The temperature dependence of first-order CDW satellite spots, obtained from the Fourier transform of the STM images, was measured between 5-140 K to extract the surface critical temperatures (T$_s$). The low T CDW transition occurs at T$_{2s}$=70-75 K, more than 15 K above the bulk T$_{2b}=59$K while at exactly the same wave number. %determined by x-ray diffraction experiments. Plausible mechanism for such an unusually high surface enhancement is a softening of transverse phonon modes involved in the CDW formation.% The large interval of the 2D regime allows to speculate on % %the special Berezinskii-Kosterlitz-Thouless type of the surface transition expected for this incommensurate CDW. This scenario is checked by extracting the temperature dependence of the order % %parameter correlation functions. The regime of 2D fluctuations is analyzed according to a Berezinskii-Kosterlitz-Thouless type of surface transition, expected for this incommensurate 2D CDW, by extracting the temperature dependence of the order parameter correlation functions.

- 1. Laboratoire de photonique et de nanostructures (LPN), CNRS : UPR20
- 2. Institut Néel (NEEL), CNRS : UPR2940 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)

**9**)## Surface Tension in Kac Glass Models

### Elia Zarinelli

^{1}, Silvio Franz^{1}#### Journal of statistical mechanics-theory and experiment (2010) P04008

In this paper we study a distance-dependent surface tension, defined as the free-energy cost to put metastable states at a given distance. This will be done in the framework of a disordered microscopic model with Kac interactions that can be solved in the mean-field limit.

## Susceptibility Propagation for Constraint Satisfaction Problems

### Saburo Higuchi

^{1}, Marc Mézard^{2}#### Journal of Physics

**233**, 1 (2010) 012003We study the susceptibility propagation, a message-passing algorithm to compute correlation functions. It is applied to constraint satisfaction problems and its accuracy is examined. As a heuristic method to find a satisfying assignment, we propose susceptibility-guided decimation where correlations among the variables play an important role. We apply this novel decimation to locked occupation problems, a class of hard constraint satisfaction problems exhibited recently. It is shown that the present method performs better than the standard belief-guided decimation.

- 1. Department of Applied Mathematics and Informatics, Ryukoku Univsersity

**5**)## Switching and growth for microbial populations in catastrophic responsive environments

### Paolo Visco

^{1}, Rosalind J. Allen^{1}, Satya N. Majumdar^{2}, Martin R. Evans^{1}#### Biophysical Journal

**98**(2010) 1099Phase variation, or stochastic switching between alternative states of gene expression, is common among microbes, and may be important in coping with changing environments. We use a theoretical model to assess whether such switching is a good strategy for growth in environments with occasional catastrophic events. We find that switching can be advantageous, but only when the environment is responsive to the microbial population. In our model, microbes switch randomly between two phenotypic states, with different growth rates. The environment undergoes sudden 'catastrophes', the probability of which depends on the composition of the population. We derive a simple analytical result for the population growth rate. For a responsive environment, two alternative strategies emerge. In the 'no switching' strategy, the population maximises its instantaneous growth rate, regardless of catastrophes. In the 'switching' strategy, the microbial switching rate is tuned to minimise the environmental response. Which of these strategies is most favourable depends on the parameters of the model. Previous studies have shown that microbial switching can be favourable when the environment changes in an unresponsive fashion between several states. Here, we demonstrate an alternative role for phase variation in allowing microbes to maximise their growth in catastrophic responsive environments.

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

**2**)## Switching and growth microbial populations in catastrophic responsive environments

### Visco, P., Allen, R.J., Majumdar, S., Evans, M.R.

#### Biophysical Journal98 (2010) 1099-1108

Details## The Hierarchical Random Energy Model

### Michele Castellana

^{1}, Aurelien Decelle^{1}, Silvio Franz^{1}, Marc Mezard^{1}, Giorgio Parisi^{2}#### Physical Review Letters

**104**(2010) 1277206We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin glass condensation transition similar to the one occuring in the usual mean field Random Energy Model. At variance with mean field, the high temperature branch of the free-energy is non-analytic at the transition point.

- 2. Dipartimento di Fisica, Università Roma I

**11**)## The Levy spin glass transition

### K. Janzen

^{1}, A. Engel^{2}, M. Mézard^{3}#### Europhysics Letters (EPL)

**89**, 6 (2010) 67002We determine the phase transition of the Levy spin glass. A regularized model where the coupling constants smaller than some cutoff $\epsilon$ are neglected can be studied by the cavity method for diluted spin glasses. We show how to handle the $\epsilon\to 0$ limit and determine the de Almeida-Thouless transition temperature in presence of an external field. Contrary to previous findings, in zero external field we do not find any stable replica-symmetric spin glass phase: the spin glass phase is always a replica-symmetry-broken phase.

- 1. Institut für Physik, Carl von Ossietzky Universität
- 2. Institut für Physik, Carl-von-Ossietzky-Universität

## The longest excursion of fractional Brownian motion : numerical evidence of non-Markovian effects

### Reinaldo Garcia-Garcia

^{1}, Alberto Rosso^{2}, Gregory Schehr^{3}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**81**(2010) 010102(R)We study, using exact numerical simulations, the statistics of the longest excursion l_{\max}(t) up to time t for the fractional Brownian motion with Hurst exponent 0 \propto Q_\infty t where Q_\infty \equiv Q_\infty(H) depends continuously on H, and in a non trivial way. These results are compared with exact analytical results obtained recently for a renewal process with an associated persistence exponent \theta = 1-H. This comparison shows that Q_\infty(H) carries the clear signature of non-Markovian effects for H\neq 1/2. The pre-asymptotic behavior of < l_{\max}(t)> is also discussed.

- 1. Centro Atomico de Bariloche, Centro Atomico de Bariloche
- 3. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud

**8**)## The universal high temperature regime of pinned elastic objects

### Sebastian Bustingorry

^{1}, Pierre Le Doussal^{2}, Alberto Rosso^{3}#### Physical Review B

**82**(2010) 140201 (R)We study the high temperature regime within the glass phase of an elastic object with short ranged disorder. In that regime we argue that the scaling functions of any observable are described by a continuum model with a $\delta$-correlated disorder and that they are universal up to only two parameters that can be explicitly computed. This is shown numerically on the roughness of directed polymer models and by dimensional and functional renormalization group arguments. We discuss experimental consequences such as non-monotonous behaviour with temperature.

- 1. CONICET, Centro Atómico Bariloche
- 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

**8**)## Thermodynamics of the Lévy spin glass

### K. Janzen

^{1}, A. Engel^{2}, M. Mézard^{3}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**82**(2010) 021127We investigate the Lévy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the model is intermediate between the Sherrington-Kirkpatrick and the Viana-Bray model. A truncated version where couplings smaller than some threshold $\eps$ are neglected can be studied within the cavity method developed for spin glasses on locally tree-like random graphs. By performing the limit $\eps\to 0$ in a well-defined way we calculate the thermodynamic functions within replica symmetry and determine the de Almeida-Thouless line in the presence of an external magnetic field. Contrary to previous findings we show that there is no replica-symmetric spin glass phase. Moreover we determine the leading corrections to the ground-state energy within one-step replica symmetry breaking. The effects due to the breaking of replica symmetry appear to be small in accordance with the intuitive picture that a few strong bonds per spin reduce the degree of frustration in the system.

- 1. Institut für Physik, Carl von Ossietzky Universität
- 2. Institut für Physik, Carl-von-Ossietzky-Universität

**4**)## Three-body problem in heteronuclear mixtures with resonant interspecies interaction

### K. Helfrich

^{1}, H. -W. Hammer^{2}, D. S. Petrov^{3, 4}#### Physical Review A: Atomic, Molecular and Optical Physics

**81**(2010) 042715We use the zero-range approximation to study a system of two identical bosons interacting resonantly with a third particle. The method is derived from effective field theory. It reduces the three-body problem to an integral equation which we then solve numerically. We also develop an alternative approach which gives analytic solutions of the integral equation in coordinate representation in the limit of vanishing total energy. The atom-dimer scattering length, the rates of atom-dimer relaxation and three-body recombination to shallow and to deep molecular states are calculated either analytically or numerically with a well controlled accuracy for various energies as functions of the mass ratio, scattering length, and three-body parameter. We discuss in detail the relative positions of the recombination loss peaks, which in the universal limit depend only on the mass ratio. Our results have implications for ongoing and future experiments on Bose-Bose and Bose-Fermi atomic mixtures.

- 1. Helmholtz-Institut für Strahlen und Kernphysik, Universität Bonn
- 2. Helmoltz Institut für Strahlen und Kernphysik, Universität Bonn
- 4. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow

**16**)## Time to reach the maximum for a random acceleration process

### Satya N. Majumdar

^{1}, Alberto Rosso^{1}, Andrea Zoia^{2}#### Journal of Physics A General Physics

**43**(2010) 115001We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present exact analytical results for the probability density $p(t_m|T)$ of the time $t_m$ at which the process reaches its maximum, within a fixed time interval $[0,T]$. We study two different boundary conditions, which correspond to the process representing respectively (i) the integral of a Brownian bridge and (ii) the integral of a free Brownian motion. Our analytical results are also verified by numerical simulations.

- 2. CEA/Saclay, CEA

**6**)## Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records

### Satya N. Majumdar

^{1}#### Physica A: Statistical Mechanics and its Applications

**389**, 20 (2010) 4299-4316In these lecture notes I will discuss the universal first-passage properties of a simple correlated discrete-time sequence {x_0=0, x_1,x_2.... x_n} up to n steps where x_i represents the position at step i of a random walker hopping on a continuous line by drawing independently, at each time step, a random jump length from an arbitrary symmetric and continuous distribution (it includes, e.g., the Levy flights). I will focus on the statistics of two extreme observables associated with the sequence: (i) its global maximum and the time step at which the maximum occurs and (ii) the number of records in the sequence and their ages. I will demonstrate how the universal statistics of these observables emerge as a consequence of Pollaczek-Spitzer formula and the associated Sparre Andersen theorem.

## Vortex structures of rotating Bose-Einstein condensates in anisotropic harmonic potential

### S. I. Matveenko

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

**82**(2010) 033628We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of anisotropic harmonic potential. For the case of symmetric harmonic trap when the rotation frequency is equal to the trapping frequency, the solution coincides with the Abrikosov triangle vortex lattice in type-II superconductors. In a general case the coarse grained density is found to be close to the Thomas-Fermi profile, except the vicinity of edges of a condensate cloud.

- 2. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics