LPTMS Publications

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• A self-consistent renormalized Jellium approach for calculating structural and thermodynamic properties of charge stabilized colloidal suspensions

Thiago E. Colla 1, Yan Levin 2, E. Trizac 3

The Journal of Chemical Physics 131 (2009) 074115

An approach is proposed which allows to self-consistently calculate the structural and thermodynamic properties of highly charged aqueous colloidal suspensions. The method is based on the renormalized Jellium model with the background charge distribution related to the colloid-colloid correlation function. The theory is used to calculate the correlation functions and the effective colloidal charges for suspension containing additional monovalent electrolyte. The predictions of the theory are in excellent agreement with the Monte Carlo simulations.

• 1. Instituto de Fisica, Universidade Federal do Rio Grande do Sul
• 2. Instituto de Física, Universidade Federal do Rio de Janeiro
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Anderson localization of a weakly interacting one dimensional Bose gas

T. Paul 1, 2, M. Albert 1, P. Schlagheck 3, 4, P. Leboeuf 1, N. Pavloff 1

Physical Review A: Atomic, Molecular and Optical Physics 80 (2009) 033615

We consider the phase coherent transport of a quasi one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow identified in [T. Paul et al., Phys. Rev. Lett. 98, 210602 (2007)], we focus here on the supersonic stationary regime where Anderson localization exists. We generalize the diffusion formalism of Dorokhov-Mello-Pereyra-Kumar to include interaction effects. It is shown that interactions modify the localization length and also introduce a length scale L* for the disordered region, above which most of the realizations of the random potential lead to time dependent flows. A Fokker-Planck equation for the probability density of the transmission coefficient that takes this new effect into account is introduced and solved. The theoretical predictions are verified numerically for different types of disordered potentials. Experimental scenarios for observing our predictions are discussed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut für Theoretische Physik, Universität Heidelberg
• 3. Institut für Theoretische Physik, Universitat Regensburg
• 4. Mathematical Physics, Lund Institute of Technology –

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• Area distribution of two-dimensional random walks on a square lattice

Stefan Mashkevich 1, 2, Stéphane Ouvry 3

Journal of Statistical Physics 137 (2009) 71-78

The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A particular case generalizes the q-binomial theorem to the case of three addends. The distribution fits the Lévy probability distribution for Brownian curves with its first-order 1/N correction quite well, even for N rather small.

• 1. Schrödinger, Schrodinger
• 2. Bogolyubov Institute for Theoretical Physics, Bogolyobov Institute for Theoretical Physics
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Asymptotic behavior of self-affine processes in semi-infinite domains

Andrea Zoia 1, Alberto Rosso 2, Satya N. Majumdar 2

Physical Review Letters 102 (2009) 120602

We propose to model the stochastic dynamics of a polymer passing through a pore (translocation) by means of a fractional Brownian motion, and study its behavior in presence of an absorbing boundary. Based on scaling arguments and numerical simulations, we present a conjecture that provides a link between the persistence exponent $\theta$ and the Hurst exponent $H$ of the process, thus sheding light on the spatial and temporal features of translocation. Furthermore, we show that this conjecture applies more generally to a broad class of self affine processes undergoing anomalous diffusion in bounded domains, and we discuss some significant examples.

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

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• Atom-dimer scattering and long-lived trimers in fermionic mixtures

J. Levinsen 1, T. G. Tiecke 2, J. T. M. Walraven 2, D. S. Petrov 1, 3

Physical Review Letters 103 (2009) 153202

We consider a heteronuclear fermionic mixture on the molecular side of an interspecies Feshbach resonance and discuss atom-dimer scattering properties in uniform space and in the presence of an external confining potential, restricting the system to a quasi-2D geometry. We find that there is a peculiar atom-dimer p-wave resonance which can be tuned by changing the frequency of the confinement. Our results have implications for the ongoing experiments on Lithium-Potassium mixtures, where this mechanism allows for switching the p-wave interaction between a K atom and Li-K dimer from attractive to repulsive, and forming a weakly bound trimer with unit angular momentum. We show that such trimers are long-lived and the atom-dimer resonance does not enhance inelastic relaxation in the mixture, making it an outstanding candidate for studies of p-wave resonance effects in a many-body system.

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

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• Avalanche-size distribution at the depinning transition: A numerical test of the theory

Alberto Rosso 1, 2, Pierre Le Doussal 1, Kay Joerg Wiese 1

Physical Review B 80 (2009) 144204

We calculate numerically the sizes S of jumps (avalanches) between successively pinned configurations of an elastic line (d=1) or interface (d=2), pulled by a spring of (small) strength m^2 in a random-field landscape. We obtain strong evidence that the size distribution, away from the small-scale cutoff, takes the form P(S) = p(S/S_m) /S_m^2, where S_m:=/(2), proportional to m^(-d-zeta), is the scale of avalanches, and zeta the roughness exponent at the depinning transition. Measurement of the scaling function f(s) := s^tau p(s) is compared with the predictions from a recent Functional RG (FRG) calculation, both at mean-field and one-loop level. The avalanche-size exponent tau is found in good agreement with the conjecture tau = 2- 2/(d+zeta), recently confirmed to one loop via the FRG. The function f(s) exhibits a shoulder and a stretched exponential decay at large s, with ln f(s) proportional to - s^delta, and delta approximately 7/6 in d=1. The function f(s), universal ratios of moments, and the generating function are found in excellent agreement with the one-loop FRG predictions. The distribution of local avalanche sizes, i.e. of the jumps of a subspace of the manifold of dimension d', is also computed and compared to our FRG predictions, and to the conjecture tau' =2- 2/(d'+zeta).

• 1. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Bogoliubov Theory of acoustic Hawking radiation in Bose-Einstein Condensates

A. Recati 1, 2, N. Pavloff 3, I. Carusotto 1

Physical Review A: Atomic, Molecular and Optical Physics 80 (2009) 043603

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations.

• 1. Università di Trento (INO-CNR BEC), UNIVERSITÀ DEGLI STUDI DI TRENTO
• 2. Physik Department, Technische Universität München
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Bridge between Abelian and Non-Abelian Fractional Quantum Hall States

N. Regnault 1, M. O. Goerbig 2, Th. Jolicoeur 3

Physical Review Letters 101 (2009) 066803

We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from K-component Halperin wave functions. In order to account for a one-component quantum Hall system, these SU(K) colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that the proposed scheme allows for a unification of both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.

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

Details Citations to the Article (19)
• Capture of particles undergoing discrete random walks

Robert M. Ziff 1, Satya N. Majumdar 2, Alain Comtet 2, 3

Journal of Chemical Physics 130, 20 (2009) 204104

It is shown that particles undergoing discrete-time jumps in 3D, starting at a distance r0 from the center of an adsorbing sphere of radius R, are captured with probability (R - c sigma)/r0 for r0 much greater than R, where c is related to the Fourier transform of the scaled jump distribution and sigma is the distribution's root-mean square jump length. For particles starting on the surface of the sphere, the asymptotic survival probability is non-zero (in contrast to the case of Brownian diffusion) and has a universal behavior sigma/(R sqrt(6)) depending only upon sigma/R. These results have applications to computer simulations of reaction and aggregation.

• 1. Michigan Center for Theoretical Physics and Department of chemical Engineering, University of Michigan-Ann Arbor
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Unite mixte de service de l'institut Henri Poincaré (UMSIHP), CNRS : UMS839 – Université Paris VI - Pierre et Marie Curie

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• Casimir interactions of an object inside a spherical metal shell

Saad Zaheer 1, Sahand Jamal Rahi 1, Thorsten Emig 2, 3, Robert L. Jaffe 1, 4

Physical Review A: Atomic, Molecular and Optical Physics 81 (2009) 030502

We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration.

• 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. Department of Physics, Center for Theoretical Physics, Massachussetts Institute of Technology (MIT)

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• Confinement Effects on the Kinetics and Thermodynamics of Protein Dimerization

Wei Wang 1, Wei-Xin Xu 1, Y. Levy 2, E. Trizac 3, P. G. Wolynes 4

Proceedings of the National Academy of Sciences of the United States of America 106 (2009) 5517-5522

In the cell, protein complexes form relying on specific interactions between their monomers. Excluded volume effects due to molecular crowding would lead to correlations between molecules even without specific interactions. What is the interplay of these effects in the crowded cellular environment? We study dimerization of a model homodimer both when the mondimers are free or tethered to each other. We consider a structured environment: Two monomers first diffuse into a cavity of size $L$ and then fold and bind within the cavity. The folding and binding are simulated using molecular dynamics based on a simplified topology based model. The {\it confinement} in the cell is described by an effective molecular concentration $C \sim L^{-3}$. A two-state coupled folding and binding behavior is found. We show the maximal rate of dimerization occurred at an effective molecular concentration $C^{op}\simeq 1m$M which is a relevant cellular concentration. In contrast, for tethered chains the rate keeps at a plateau when $CC^{op}$. For both the free and tethered cases, the simulated variation of the rate of dimerization and thermodynamic stability with effective molecular concentration agrees well with experimental observations. In addition, a theoretical argument for the effects of confinement on dimerization is also made.

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

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• Convex Hull of N Planar Brownian Motions: Exact Results and an Application to Ecology

Julien Randon-Furling 1, Satya N. Majumdar 1, Alain Comtet 1, 2

Physical Review Letters 103 (2009) 140602

We compute exactly the mean perimeter and area of the convex hull of N independent planar Brownian paths each of duration T, both for open and closed paths. We show that the mean perimeter < L_N > = \alpha_N, \sqrt{T} and the mean area = \beta_N T for all T. The prefactors \alpha_N and \beta_N, computed exactly for all N, increase very slowly (logarithmically) with increasing N. This slow growth is a consequence of extreme value statistics and has interesting implication in ecological context in estimating the home range of a herd of animals with population size N.

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

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• Creep dynamics of elastic manifolds via exact transition pathways

Alejandro B. Kolton 1, Alberto Rosso 2, Thierry Giamarchi 3, Werner Krauth 4

Physical Review B 79 (2009) 184207

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.

• 1. Centro Atomico Bariloche, Centro Atómico Bariloche
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. DPMC (DPMC-MaNEP), University of Geneva
• 4. Laboratoire de Physique Statistique de l'ENS (LPS), CNRS : UMR8550 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – Ecole Normale Supérieure de Paris - ENS Paris

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• Critical properties of 1D spin-gapped fermions at the onset of magnetization

T. Vekua 1, S. I. Matveenko 1, 2, G. V. Shlyapnikov 1, 3

JETP Letters / Sov Phys JETP Lett 90 (2009) 289-294

We develop an effective field theory for finding critical properties of 1D spin gapped fermions at the onset of magnetization. It is shown how the spin-charge interaction leads to a linear critical behavior and finite susceptibility for a wide range of models. We also discuss possible manifestations of spin-charge coupling in cold atomic gases.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
• 3. Van der Waals-Zeeman Institute, University of Amsterdam

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• Decimation flows in constraint satisfaction problems

Saburo Higuchi 1, Marc Mézard 2

Journal of statistical mechanics-theory and experiment (2009) P12009

We study hard constraint satisfaction problems with a decimation approach based on message passing algorithms. Decimation induces a renormalization flow in the space of problems, and we exploit the fact that this flow transforms some of the constraints into linear constraints over GF(2). In particular, when the flow hits the subspace of linear problems, one can stop decimation and use Gaussian elimination. We introduce a new decimation algorithm which uses this linear structure and shows a strongly improved performance with respect to the usual decimation methods on some of the hardest locked occupation problems.

• 1. Department of Applied Mathematics and Informatics, Ryukoku Univsersity
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Density ripples in expanding low-dimensional gases as a probe of correlations

A. Imambekov 1, 2, I. E. Mazets 3, 4, D. S. Petrov 5, 6, V. Gritsev 7, S. Manz 3, S. Hofferberth 8, T. Schumm 3, 9, E. Demler 8, J. Schmiedmayer 3

Physical Review A: Atomic, Molecular and Optical Physics 80 (2009) 033604

We investigate theoretically the evolution of the two-point density correlation function of a low-dimensional ultracold Bose gas after release from a tight transverse confinement. In the course of expansion thermal and quantum fluctuations present in the trapped systems transform into density fluctuations. For the case of free ballistic expansion relevant to current experiments, we present simple analytical relations between the spectrum of density ripples'' and the correlation functions of the original confined systems. We analyze several physical regimes, including weakly and strongly interacting one-dimensional (1D) Bose gases and two-dimensional (2D) Bose gases below the Berezinskii-Kosterlitz-Thouless (BKT) transition. For weakly interacting 1D Bose gases, we obtain an explicit analytical expression for the spectrum of density ripples which can be used for thermometry. For 2D Bose gases below the BKT transition, we show that for sufficiently long expansion times the spectrum of the density ripples has a self-similar shape controlled only by the exponent of the first-order correlation function. This exponent can be extracted by analyzing the evolution of the spectrum of density ripples as a function of the expansion time.

• 1. Department of Physics, Yale University
• 2. Department of Physics and Astronomy, Rice University
• 3. Atominstitut, Fakiltat fur Physik
• 4. Ioffe Physico-Technical Institute, Ioffe Physico-Technical Institute
• 5. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 6. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow
• 7. Physics Department, University of Fribourg
• 8. Department of Physics, University of Harvard
• 9. Wolfgang Pauli Institute (WPI), University of Vienna

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• Energy fluctuations in a randomly driven granular fluid

M. I. Garcia de Soria 1, P. Maynar 2, 3, E. Trizac 1

Molecular Physics 107, 4 (2009) 383-392

We study the behavior of the energy fluctuations in the stationary state of a uniformly heated granular gas. The equation for the one-time two-particle correlation function is derived and the hydrodynamic eigenvalues are identified. Explicit predictions are subsequently worked out for energy fluctuations. The results explain Monte Carlo numerical data reported in previous studies (P. Visco et al, European Physical Journal B 51, 377 (2006)).

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud

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• Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant

O. Benichou 1, J. Desbois 2

Journal of Physics A Mathematical and Theoretical 42 (2009) 015004

We consider a particle diffusing along the links of a general graph possessing some absorbing vertices. The particle, with a spatially-dependent diffusion constant D(x) is subjected to a drift U(x) that is defined in every point of each link. We establish the boundary conditions to be used at the vertices and we derive general expressions for the average time spent on a part of the graph before absorption and, also, for the Laplace transform of the joint law of the occupation times. Exit times distributions and splitting probabilities are also studied and several examples are discussed.

• 1. Laboratoire de Physique Théorique des Liquides (LPTL), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Fluctuating hydrodynamics for dilute granular gases

J. Javier Brey 1, P. Maynar 1, 2, M. I. Garcia de Soria 1, 3

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 79 (2009) 051305

Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is constructed. This equation is the linear Boltzmann equation with a fluctuating white noise term. Balance equations for the fluctuating hydrodynamic fields are derived. New fluctuating forces appear as compared with the elastic limit. The particular case of the transverse velocity field is investigated in detail. Its fluctuations can be described by means of a Langevin equation, but exhibiting two main differences with the Landau-Lifshitz theory: the noise is not white, and its second moment is not determined by the shear viscosity. This shows that the fluctuation-dissipation relations for molecular fluids do not straightforwardly carry over to inelastic gases. The theoretical predictions are shown to be in good agreement with molecular dynamics simulation results.

• 2. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Fluctuating hydrodynamics for driven granular gases

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

The European Physical Journal Special Topics 179, 1 (2009) 123-139

We study a granular gas heated by a stochastic thermostat in the dilute limit. Starting from the kinetic equations governing the evolution of the correlation functions, a Boltzmann-Langevin equation is constructed. The spectrum of the corresponding linearized Boltzmann-Fokker-Planck operator is analyzed, and the equation for the fluctuating transverse velocity is derived in the hydrodynamic limit. The noise term (Langevin force) is thus known microscopically and contains two terms: one coming from the thermostat and the other from the fluctuating pressure tensor. At variance with the free cooling situation, the noise is found to be white and its amplitude is evaluated.

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

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• Ground State and Excitations of Quantum Dots with ‘Magnetic Impurities’

R. K. Kaul 1, 2, D. Ullmo 3, G. Zarand 4, 5, S. Chandrasekharan 6, H. U. Baranger 6

Physical Review B 80 (2009) 035318

We consider an 'impurity' with a spin degree of freedom coupled to a finite reservoir of non-interacting electrons, a system which may be realized by either a true impurity in a metallic nano-particle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong and weak coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity susceptibility and the local susceptibility. Extensive quantum Monte-Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir -- the 'clean Kondo box' model -- we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parity and for the canonical and grand-canonical ensembles.

• 1. Institut fur Theorie der Kondensierten Materie, Universität Karlsruhe
• 2. Department of Physics, Duke University
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Research Institute of Physics, Technical University Budapest
• 5. Institüt für Theoretische Fesköperphysik, Universität Karlsruh
• 6. Duke Physics, Duke University

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• Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnets

Revaz Ramazashvili 1, 2

Physical Review B 79 (2009) 184432

In this article, I analyze the symmetries and degeneracies of electron eigenstates in a commensurate collinear antiferromagnet. In a magnetic field transverse to the staggered magnetization, a hidden anti-unitary symmetry protects double degeneracy of the Bloch eigenstates at a special set of momenta. In addition to this Kramers degeneracy' subset, the manifold of momenta, labeling the doubly degenerate Bloch states in the Brillouin zone, may also contain an accidental degeneracy' subset, that is not protected by symmetry and that may change its shape under perturbation. These degeneracies give rise to a substantial momentum dependence of the transverse g-factor in the Zeeman coupling, turning the latter into a spin-orbit interaction. I discuss a number of materials, where Zeeman spin-orbit coupling is likely to be present, and outline the simplest properties and experimental consequences of this interaction, that may be relevant to systems from chromium to borocarbides, cuprates, hexaborides, iron pnictides, as well as organic and heavy fermion conductors.

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

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• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices

Satya N. Majumdar 1, Massimo Vergassola 2

Physical Review Letters 102 (2009) 060601

We present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is quite general and applies to other related problems, e.g. the joint large deviation function for large fluctuations of top eigenvalues. Our results are relevant to widely employed data compression techniques, namely the principal components analysis. Analytical predictions are verified by extensive numerical simulations.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Génétique in Silico, CNRS : URA2171 – Institut Pasteur de Paris

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• Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices

G. Orso 1, A. Iucci 2, 3, M. A. Cazalilla 4, 5, T. Giamarchi 3

Physical Review A: Atomic, Molecular and Optical Physics 80 (2009) 033625

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasi-periodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the non-commensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly we find that a perturbative treatment in both cases, weak and strong disorder, gives a good description at all frequencies. In particular we find that the infrared absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected, since for other quantities like the conductivity in one dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems, and in particular the effect of the harmonic trap.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Instituto de Fisica la Plata (IFLP), Universidad Nacional de la Plata
• 3. DPMC-MaNEP, University of Geneva, University of Geneva
• 4. Centro de Fisica de Materiales (CSIS-UPV/EHU), University San Sebastian
• 5. Donostia International Physics Center (DIPC), University San Sebastian

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• Littlewood–Richardson coefficients and integrable tilings

Paul Zinn-Justin 1

The Electronic Journal of Combinatorics 16 (2009) R12

We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood--Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur functions, allowing in particular to recover formulae of [Molev--Sagan '99] and [Knutson--Tao '03] for factorial Schur functions. The method is based on the quantum integrability of the underlying tiling model.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot

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• Message Passing for Optimization and Control of Power Grid: Model of Distribution System with Redundancy

Lenka Zdeborová 1, Aurélien Decelle 2, Michael Chertkov 3

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 80 (2009) 046112

We use a power grid model with $M$ generators and $N$ consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load fluctuations. Each generator has a maximum power capability. A generator is not overloaded if the sum of the loads of consumers connected to a generator does not exceed its maximum production. In the standard grid each consumer is connected only to its designated generator, while we consider a more general organization of the grid allowing each consumer to select one generator depending on the load from a pre-defined consumer-dependent and sufficiently small set of generators which can all serve the load. The model grid is interconnected in a graph with loops, drawn from an ensemble of random bipartite graphs, while each allowed configuration of loaded links represent a set of graph covering trees. Losses, the reactive character of the grid and the transmission-level connections between generators (and many other details relevant to realistic power grid) are ignored in this proof-of-principles study. We focus on the asymptotic limit and we show that the interconnects allow significant expansion of the parameter domains for which the probability of a generator overload is asymptotically zero. Our construction explores the formal relation between the problem of grid optimization and the modern theory of sparse graphical models. We also design heuristic algorithms that achieve the asymptotically optimal selection of loaded links. We conclude discussing the ability of this approach to include other effects, such as a more realistic modeling of the power grid and related optimization and control algorithms.

• 1. Center for Nonlinear Studies and Theoretical Division, Center for Nonlinear Studies and Theoretical Division
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Center for Nonlinear Studies and Theoretical Division, Center for Nonlinear Studies and Theoretical Division

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• Modified Coulomb gas construction of quantum Hall states from non-unitary conformal field theories

M. V. Milovanović 1, Th. Jolicoeur 2, I. Vidanović 3

Physical Review B 80 (2009) 155324

Some fractional quantum Hall states observed in experiments may be described by first-quantized wavefunctions with special clustering properties like the Moore-Read Pfaffian for filling factor nu = 5/2. This wavefunction has been constructed by constructing correlation functions of a two-dimensional conformal field theory (CFT) involving a free boson and a Majorana fermion. By considering other CFTs many other clustered states have been proposed as candidate FQH states under appropriate circumstances. It is believed that the underlying CFT should be unitary if one wants to describe an incompressible i.e. gapped liquid state. We show that by changing the way one derives the wavefunction from its parent CFT it is possible to obtain an incompressible candidate state when starting from a non-unitary parent. The construction mimics a global change of parameters in the phase space of the electron system. We explicit our construction in the case of the so-called Gaffnian state (a state for filling factor 2/5) and also for the Haldane-Rezayi state (a spin-singlet state at filling 1/2).

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

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• Multi-particle composites in density-imbalanced quantum fluids

Evgeni Burovski 1, Giuliano Orso 1, Thierry Jolicoeur 1

Physical Review Letters 103 (2009) 215301

We consider two-component one-dimensional quantum gases with density imbalance. While generically such fluids are two-component Luttinger liquids, we show that if the ratio of the densities is a rational number, p/q, and mass asymmetry between components is sufficiently strong, one of the two eigenmodes acquires a gap. The gapped phase corresponds to (algebraic) ordering of (p+q)-particle composites. In particular, for attractive mixtures, this implies that the superconducting correlations are destroyed. We illustrate our predictions by numerical simulations of the fermionic Hubbard model with hopping asymmetry.

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

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• Near integrable systems

E. Bogomolny 1, M. R. Dennis 2, R. Dubertrand 3

Journal of Physics A Mathematical and Theoretical 42 (2009) 335102

A two-dimensional circular quantum billiard with unusual boundary conditions introduced by Berry and Dennis (\emph{J Phys A} {\bf 41} (2008) 135203) is considered in detail. It is demonstrated that most of its eigenfunctions are strongly localized and the corresponding eigenvalues are close to eigenvalues of the circular billiard with Neumann boundary conditions. Deviations from strong localization are also discussed. These results agree well with numerical calculations.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. H H Wills Physics Laboratory, Wills Physics Laboratory
• 3. Department of Mathematics [Bristol], University of Bristol – University Walk

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• Non-intersecting Brownian Interfaces and Wishart Random Matrices

Céline Nadal 1, Satya N. Majumdar 1

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 79 (2009) 061117

We study a system of $N$ non-intersecting $(1+1)$-dimensional fluctuating elastic interfaces (`vicious bridges') at thermal equilibrium, each subject to periodic boundary condition in the longitudinal direction and in presence of a substrate that induces an external confining potential for each interface. We show that, for a large system and with an appropriate choice of the external confining potential, the joint distribution of the heights of the $N$ non-intersecting interfaces at a fixed point on the substrate can be mapped to the joint distribution of the eigenvalues of a Wishart matrix of size $N$ with complex entries (Dyson index $\beta=2$), thus providing a physical realization of the Wishart matrix. Exploiting this analogy to random matrix, we calculate analytically (i) the average density of states of the interfaces (ii) the height distribution of the uppermost and lowermost interfaces (extrema) and (iii) the asymptotic (large $N$) distribution of the center of mass of the interfaces. In the last case, we show that the probability density of the center of mass has an essential singularity around its peak which is shown to be a direct consequence of a phase transition in an associated Coulomb gas problem.

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

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• Non-local pair correlations in the 1D Bose gas at finite temperature

P. Deuar 1, A. G. Sykes 2, D. M. Gangardt 3, M. J. Davis 4, P. D. Drummond 5, K. V. Kheruntsyan 6

Physical Review A: Atomic, Molecular and Optical Physics 79 (2009) 043619

The behavior of the spatial two-particle correlation function is surveyed in detail for a uniform 1D Bose gas with repulsive contact interactions at finite temperatures. Both long-, medium-, and short-range effects are investigated. The results span the entire range of physical regimes, from ideal gas, to strongly interacting, and from zero temperature to high temperature. We present perturbative analytic methods, available at strong and weak coupling, and first-principle numerical results using imaginary time simulations with the gauge-P representation in regimes where perturbative methods are invalid. Nontrivial effects are observed from the interplay of thermally induced bunching behavior versus interaction induced antibunching.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Centre of excellence for quantum atom optics (ARC), University of Queensland
• 3. School of Physics and Astronomy, University of Birmingham, University of Birmingham
• 4. Centre of excellence for quantum atom optics (ARC), University of Queensland
• 5. ARC Centre of Excellence for Quantum Atom Optics, Swin burne University of Technology
• 6. Centre of excellence for quantum atom optics (ARC), University of Queensland

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• Non-neutral theory of biodiversity

Ginestra Bianconi 1, Luca Ferretti 2, Silvio Franz 3

Europhysics Letters (EPL) 87 (2009) 28001

We present a non-neutral stochastic model for the dynamics taking place in a meta-community ecosystems. The model provides a framework for describing the emergence of multiple ecological scenarios and behaves in two extreme limits either as the unified neutral theory of biodiversity or as the Bak-Sneppen model. Interestingly, the model shows a condensation phase transition where one species becomes the dominant one, the diversity in the ecosystems is strongly reduced and the ecosystem is non-stationary. This phase transition extend the principle of competitive exlusion to open ecosystems and might be relevant for the study of the impact of invasive species in native ecologies.

• 1. The Abdus Salam International Centre for Theoretical Physics, ICTP Trieste
• 2. Facultat de Veterinaria and IFAE, Universitat Autónoma de Barcelona
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Off-diagonal correlations in one-dimensional anyonic models: A replica approach

Pasquale Calabrese 1, Raoul Santachiara 2

Journal of statistical mechanics-theory and experiment March 2009, 03 (2009) P03002

We propose a generalization of the replica trick that allows to calculate the large distance asymptotic of off-diagonal correlation functions in anyonic models with a proper factorizable ground-state wave-function. We apply this new method to the exact determination of all the harmonic terms of the correlations of a gas of impenetrable anyons and to the Calogero Sutherland model. Our findings are checked against available analytic and numerical results.

• 1. Dipartimento di Fisica dell'Universita di Pisa and INFN,Pisa, UNIVERSITÀ DEGLI STUDI DI PISA
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• On scale-free and poly-scale behaviors of random hierarchical network

V. A. Avetisov 1, A. V. Chertovich 2, S. K. Nechaev 3, 4, O. A. Vasilyev 5, 6

Journal of Statistical Mechanics (2009) P07008

In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In particular, we compute numerically the spectral density of large random adjacency matrices defined by a hierarchy of the Bernoulli distributions $\{q_1,q_2,...\}$ on matrix elements, where $q_{\gamma}$ depends on hierarchy level $\gamma$ as $q_{\gamma}=p^{-\mu \gamma}$ ($\mu>0$). For the spectral density we clearly see the free--scale behavior. We show also that for the Gaussian distributions on matrix elements with zero mean and variances $\sigma_{\gamma}=p^{-\nu \gamma}$, the tail of the spectral density, $\rho_G(\lambda)$, behaves as $\rho_G(\lambda) \sim |\lambda|^{-(2-\nu)/(1-\nu)}$ for $|\lambda|\to\infty$ and $0<\nu<1$, while for $\nu\ge 1$ the power--law behavior is terminated. We also find that the vertex degree distribution of such hierarchical networks has a poly--scale fractal behavior extended to a very broad range of scales.

• 1. The Semenov Institute of Chemical Physics, Russian Academy of Sciences
• 2. Physics Department, Moscow State University
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. P. N. Lebedev Physical Institute, Russian Academy of Science
• 5. Max-Planck-Institute für Metallforschung, Max-Planck-Institut
• 6. Institut für Theoretische and Angewandte Physik, Universität Stuttgart

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• On some ground state components of the O(1) loop model

T. Fonseca 1, Paul Zinn-Justin 1

Journal of Statistical Mechanics (2009) P03025

We address a number of conjectures about the ground state O(1) loop model, computing in particular two infinite series of partial sums of its entries and relating them to the enumeration of plane partitions. Our main tool is the use of integral formulae for a polynomial solution of the quantum Knizhnik-Zamolodchikov equation.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot

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• On the Lieb-Liniger model in the infinite coupling constant limit

Stephane Ouvry 1, Alexios P. Polychronakos 2

Journal of Physics A Mathematical and Theoretical 42 (2009) 275302

We consider the one-dimensional Lieb-Liniger model (bosons interacting via 2-body delta potentials) in the infinite coupling constant limit (the so-called Tonks-Girardeau model). This model might be relevant as a description of atomic Bose gases confined in a one-dimensional geometry. It is known to have a fermionic spectrum since the N-body wavefunctions have to vanish at coinciding points, and therefore be symmetrizations of fermionic Slater wavefunctions. We argue that in the infinite coupling constant limit the model is indistinguishable from free fermions, i.e., all physically accessible observables are the same as those of free fermions. Therefore, Bose-Einstein condensate experiments at finite energy that preserve the one-dimensional geometry cannot test any bosonic characteristic of such a model.

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

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• One-dimensional classical diffusion in a random force field with weakly concentrated absorbers

Christophe Texier 1, Christian Hagendorf 2

Europhysics Letters (EPL) 86 (2009) 37011

A one-dimensional model of classical diffusion in a random force field with a weak concentration $\rho$ of absorbers is studied. The force field is taken as a Gaussian white noise with $\mean{\phi(x)}=0$ and $\mean{\phi(x)\phi(x')}=g \delta(x-x')$. Our analysis relies on the relation between the Fokker-Planck operator and a quantum Hamiltonian in which absorption leads to breaking of supersymmetry. Using a Lifshits argument, it is shown that the average return probability is a power law $\smean{P(x,t|x,0)}\sim{}t^{-\sqrt{2\rho/g}}$ (to be compared with the usual Lifshits exponential decay $\exp{-(\rho^2t)^{1/3}}$ in the absence of the random force field). The localisation properties of the underlying quantum Hamiltonian are discussed as well.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

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• Pairing in ultracold Fermi gases in the lowest landau level

G. Moller 1, Th. Jolicoeur 2, N. Regnault 3

Physical Review A: Atomic, Molecular and Optical Physics 79 (2009) 033609

We study a rapidly rotating gas of unpolarized spin-1/2 ultracold fermions in the two-dimensional regime when all atoms reside in the lowest Landau level. Due to the presence of the spin degree of freedom both s-wave and p-wave interactions are allowed at ultralow temperatures. We investigate the phase diagram of this system as a function of the filling factor of the lowest Landau level and of the ratio between s- and p-wave interaction strengths. We show that the presence of attractive interactions induces a wide regime of phase separation with formation of maximally compact droplets that are either fully polarized or spin-singlet. When there is no phase separation, we give evidence for fractional quantum Hall states. Most notably we find that at the filling nu = 2/3 there is a singlet state accounted for by composite fermion theory which competes with an Abelian state of composite spin-singlet Bose molecules with Laughlin correlations. By fine tuning of the scattering lengths it is possible to create the non-Abelian critical Haldane-Rezayi state for nu = 1/2 and the permanent state of Moore and Read for nu = 1. For purely repulsive interactions, we also find evidence for a gapped Halperin state at nu = 2/5.

• 1. TCM Group, Cavendish Laboratory, Cavendish Laboratory Cambridge
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. 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

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• Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State

Celine Nadal 1, Satya N. Majumdar 1, Massimo Vergassola 2

Physical Review Letters 104 (2009) 110501

Using a Coulomb gas method, we compute analytically the probability distribution of the Renyi entropies (a standard measure of entanglement) for a random pure state of a large bipartite quantum system. We show that, for any order q>1 of the Renyi entropy, there are two critical values at which the entropy's probability distribution changes shape. These critical points correspond to two different transitions in the corresponding charge density of the Coulomb gas: the disappearance of an integrable singularity at the origin and the detachement of a single-charge drop from the continuum sea of all the other charges. These transitions respectively control the left and right tails of the entropy's probability distribution, as verified also by Monte Carlo numerical simulations of the Coulomb gas equilibrium dynamics.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Génétique in Silico, CNRS : URA2171 – Institut Pasteur de Paris

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• Pinning of Flux Lines by Planar Defects

Aleksandra Petkovic 1, Thorsten Emig 1, 2, Thomas Nattermann 1

Physical Review B 79, 22 (2009) 224512

The influence of randomly distributed point impurities and planar defects on order and transport in type-II superconductors and related systems is studied. It is shown that the Bragg glass phase is unstable with respect to planar efects. Even a single weak defect plane oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is a relevant perturbation in the Bragg glass. A defect that is aligned with the magnetic field restores the flux density oscillations which decay algebraically with the distance from the defect. The theory exhibits striking similarities to the physics of a Luttinger liquid with a frozen impurity. The exponent for the flux line creep in the direction perpendicular to a relevant defect is derived. We find that the flux line lattice exhibits in the presence of many randomly distributed parallel planar defects aligned to the magnetic field a new glassy phase which we call planar glass. The planar glass is characterized by diverging shear and tilt moduli, a transverse Meissner effect, resistance against shear deformations. We also obtain sample to sample fluctuations of the longitudinal magnetic susceptibility and an exponential decay of translational long range order in the direction perpendicular to the defects. The flux creep perpendicular to the defects leads to a nonlinear resistivity $\rho(J \to 0)\sim \exp[-(J_D/J)^{3/2}]$. Strong planar defects enforce arrays of dislocations that are located at the defects with a Burgers vector parallel to the defects in order to relax shear strain.

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

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• Polarization induced instabilities in external four-mirror Fabry-Perot cavities

F. Zomer 1, Y. Fedala 1, N. Pavloff 2, V. Soskov 1, A. Variola 1

Applied Optics 48 (2009) 6651-6661

Various four-mirror optical resonators are studied in the perspective of realizing passive stacking cavities. A comparative study of the mechanical stability is provided. The polarization properties of the cavity eigenmodes are described and it is shown that the effect of mirror misalignments (or motions) induces polarization and stacking power instabilities. These instabilities increase with the finesse of the Fabry-Perot cavity. A tetrahedral configuration of the four mirrors is found to minimize the consequences of the mirrors's motion and misalignment by reducing the instability parameter by at least two orders of magnitude

• 1. Laboratoire de l'Accélérateur Linéaire (LAL), CNRS : UMR8607 – IN2P3 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders

Christophe Texier 1, 2, Pierre Delplace 2, Gilles Montambaux 2

Physical Review B 80 (2009) 205413

We have studied the quantum oscillations of the conductance for arrays of connected mesoscopic metallic rings, in the presence of an external magnetic field. Several geometries have been considered: a linear array of rings connected with short or long wires compared to the phase coherence length, square networks and hollow cylinders. Compared to the well-known case of the isolated ring, we show that for connected rings, the winding of the Brownian trajectories around the rings is modified, leading to a different harmonics content of the quantum oscillations. We relate this harmonics content to the distribution of winding numbers. We consider the limits where coherence length $L_\varphi$ is small or large compared to the perimeter $L$ of each ring constituting the network. In the latter case, the coherent diffusive trajectories explore a region larger than $L$, whence a network dependent harmonics content. Our analysis is based on the calculation of the spectral determinant of the diffusion equation for which we have a simple expression on any network. It is also based on the hypothesis that the time dependence of the dephasing between diffusive trajectories can be described by an exponential decay with a single characteristic time $\tau_\varphi$ (model A) . At low temperature, decoherence is limited by electron-electron interaction, and can be modelled in a one-electron picture by the fluctuating electric field created by other electrons (model B). It is described by a functional of the trajectories and thus the dependence on geometry is crucial. Expressions for the magnetoconductance oscillations are derived within this model and compared to the results of model A. It is shown that they involve several temperature-dependent length scales.

• 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

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• Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined

Guillaume Roux 1, 2

Physical Review A: Atomic, Molecular and Optical Physics 79 (2009) 021608

When a quantum many-body system undergoes a quench, the time-averaged density-matrix $\rho$ governs the time-averaged expectation value of any observable. It is therefore the key object to look at when comparing results with equilibrium predictions. We show that the weights of $\rho$ can be efficiently computed with Lanczos diagonalization for relatively large Hilbert spaces. As an application, we investigate the crossover from perturbative to non-perturbative quenches in the non-integrable Bose-Hubbard model: on finite systems, an approximate Boltzmann distribution is observed for small quenches, while for larger ones the distributions do not follow standard equilibrium predictions. Studying thermodynamical features, such as the energy fluctuations and the entropy, shows that $\rho$ bears a memory of the initial state.

• 1. Institute for Theoretical Physics, Aachen University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees

V. A. Avetisov 1, A. Kh. Bikulov 2, S. K. Nechaev 3

Journal of Physics A Mathematical and Theoretical 42 (2009) 075001

We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to 'locally constant' randomization. Using the explicit expression for eigenvalues of such matrices, we compute the spectral density for the Gaussian distribution of matrix elements. We also compute the averaged 'survival probability' (SP) having sense of the probability to find a system in the initial state by time $t$. Using the similarity between the averaged SP for locally constant randomized Parisi matrices and the partition function of directed polymers on disordered trees, we show that for times $t>t_{\rm cr}$ (where $t_{\rm cr}$ is some critical time) a 'lacunary' structure of the ultrametric space occurs with the probability $1-{\rm const}/t$. This means that the escape from some bounded areas of the ultrametric space of states is locked and the kinetics is confined in these areas for infinitely long time.

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

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• Random matrix ensembles associated with Lax matrices

E. Bogomolny 1, Olivier Giraud 2, C. Schmit 1

Physical Review Letters 103 (2009) 054103

A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an integrable structure permits to calculate the joint distribution of eigenvalues for these matrices analytically. Spectral statistics of these ensembles are quite unusual and in many cases give rigorously new examples of intermediate statistics.

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

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• Random-Matrix Approach to RPA equations. I

X. Barillier-Pertuisel 1, O. Bohigas 2, H. A. Weidenmueller 3

Annals of Physics 324, 9 (2009) 1855-1874

We study the RPA equations in their most general form by taking the matrix elements appearing in the RPA equations as random. This yields either a unitarily or an orthogonally invariant random-matrix model which is not of the Cartan type. The average spectrum of the model is studied with the help of a generalized Pastur equation. Two independent parameters govern the behaviour of the system: The strength $\alpha^2$ of the coupling between positive- and negative-energy states and the distance between the origin and the centers of the two semicircles that describe the average spectrum for $\alpha^2 = 0$, the latter measured in units of the equal radii of the two semicircles. With increasing $\alpha^2$, positive- and negative-energy states become mixed and ever more of the spectral strength of the positive-energy states is transferred to those at negative energy, and vice versa. The two semicircles are deformed and pulled toward each other. As they begin to overlap, the RPA equations yield non--real eigenvalues: The system becomes unstable. We determine analytically the critical value of the strength for the instability to occur. Several features of the model are illustrated numerically.

• 1. Institut de Physique Nucléaire d'Orsay (IPNO), CNRS : UMR8608 – IN2P3 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Max-Planck-Institute für Kernphysik, Max-Planck-Institut

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• Relating Jack wavefunctions to WA_{k-1} theories

Benoit Estienne 1, Raoul Santachiara 2

Journal of Physics A Mathematical and Theoretical 42 (2009) 445209

The (k,r)-admissible Jack polynomials, recently proposed as many-body wavefunctions for non-Abelian fractional quantum Hall systems, have been conjectured to be related to some correlation functions of the minimal model WA_{k-1}(k+1,k+r) of the WA_{k-1} algebra. By studying the degenerate representations of the WA_{k-1}(k+1,k+r) theory, we provide a proof for this conjecture.

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

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• Return probabilities and hitting times of random walks on sparse Erdos-Renyi graphs

O. C. Martin 1, 2, P. Sulc 1

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 81 (2009) 031111

We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. We show how to solve for the distribution of these quantities in the thermodynamic limit and we find that these distributions exhibit structures on all scales.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Génétique Végétale (GV), CNRS : UMR8120 – Institut national de la recherche agronomique (INRA) : UMR0320 – Université Paris XI - Paris Sud – Institut National Agronomique Paris-Grignon

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• Scattering Theory Approach to Electrodynamic Casimir Forces

Sahand Jamal Rahi 1, 2, Thorsten Emig 1, 2, 3, 4, Noah Graham 5, Robert L. Jaffe 1, 6, Mehran Kardar 1, 7

Physical Review D 80 (2009) 085021

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, nonzero temperatures, and 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. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

• 1. Department of Physics, Massachusetts Institute of Technology
• 2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara
• 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. Middlebury College, Middlebury Colleg
• 6. Department of Physics, Center for Theoretical Physics, Massachussetts Institute of Technology (MIT)
• 7. Kavli Institute for Theoretical Institute, University of California, Santa Barbara

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• Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybrids

Piotr Deuar 1

Physical Review Letters 103 (2009) 130402

A controlled hybridization between full quantum dynamics and semiclassical approaches (mean-field and truncated Wigner) is implemented for interacting many-boson systems. It is then demonstrated how simulating the resulting hybrid evolution equations allows one to obtain the full quantum dynamics for much longer times than is possible using an exact treatment directly. A collision of sodium BECs with 1.x10^5 atoms is simulated, in a regime that is difficult to describe semiclassically. The uncertainty of physical quantities depends on the statistics of the full quantum prediction. Cutoffs are minimised to a discretization of the Hamiltonian. The technique presented is quite general and extension to other systems is considered.

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

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• Spectral statistics of a pseudo-integrable map: the general case

E. Bogomolny 1, R. Dubertrand 1, 2, C. Schmit 1

Nonlinearity 22 (2009) 2101-2126

It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In [PRL,93 (2004) 254102] statistical properties of a certain quantized pseudo-integrable map had been calculated analytically but only for a special sequence of matrix dimensions. The purpose of this paper is to obtain the spectral statistics of the same quantum map for all matrix dimensions.

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

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• Stability and pairing in quasi-one-dimensional Bose-Fermi mixtures

F. M. Marchetti 1, Th. Jolicoeur 2, M. M. Parish 3

Physical Review Letters 103 (2009) 105304

We consider a mixture of single-component bosonic and fermionic atoms in an array of coupled one-dimensional 'tubes'. For an attractive Bose-Fermi interaction, we show that the system exhibits phase separation instead of the usual collapse. Moreover, above a critical inter-tube hopping, all first-order instabilities disappear in both attractive and repulsive mixtures. The possibility of suppressing instabilities in this system suggests a route towards the realization of paired phases, including a superfluid of p-wave pairs unique to the coupled-tube system, and quantum critical phenomena.

• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Princeton Center for Theorical Science, Princeton University

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• Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules

N. R. Cooper 1, 2, G. V. Shlyapnikov 2, 3

Physical Review Letters 103 (2009) 155302

We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field, may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+ip_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim 10^8$ cm$^{-2}$.

• 1. TCM Group, Cavendish Laboratory, Cavendish Laboratory Cambridge
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Van der Waals-Zeeman Institute, University of Amsterdam

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• Statistical Mechanics of Logarithmic REM: Duality, Freezing and Extreme Value Statistics of $1/f$ Noises generated by Gaussian Free Fields

Yan V Fyodorov 1, Pierre Le Doussal 2, Alberto Rosso 3

Journal of statistical mechanics-theory and experiment (2009) P10005

We compute the distribution of the partition functions for a class of one-dimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the two-dimensional Gaussian Free Field (2dGFF) along various planar curves. Our method extends the recent analysis of Fyodorov Bouchaud from the circular case to an interval and is based on an analytical continuation of the Selberg integral. In particular, we unveil a {\it duality relation} satisfied by the suitable generating function of free energy cumulants in the high-temperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2dGFF on the $[0,1]$ interval. We provide numerical checks of the circular and the interval case and discuss universality and various extensions. Relevance to the distribution of length of a segment in Liouville quantum gravity is noted.

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

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• The Index Distribution of Gaussian Random Matrices

Satya N. Majumdar 1, Celine Nadal 1, Antonello Scardicchio 2, Pierpaolo Vivo 2

Physical Review Letters 103 (2009) 220603

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N_{+}/N scales, for large N, as Prob(c,N)\simeq\exp[-\beta N^2 \Phi(c)] where the rate function \Phi(c), symmetric around c=1/2 and universal (independent of $\beta$), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. The Abdus Salam International Centre for Theoretical Physics, ICTP Trieste

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• Three-body Casimir effects and non-monotonic forces

P. Rodriguez-Lopez 1, S. J. Rahi 2, T. Emig 3, 4

Physical Review A: Atomic, Molecular and Optical Physics 80 (2009) 022519

Casimir interactions are not pair-wise additive. This property leads to collective effects that we study for a pair of objects near a conducting wall. We employ a scattering approach to compute the interaction in terms of fluctuating multipoles. The wall can lead to a non-monotonic force between the objects. For two atoms with anisotropic electric and magnetic dipole polarizabilities we demonstrate that this non-monotonic effect results from a competition between two- and three body interactions. By including higher order multipoles we obtain the force between two macroscopic metallic spheres for a wide range of sphere separations and distances to the wall.

• 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

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• Vortex structures in rotating Bose-Einstein condensates

S. I. Matveenko 1, 2, D. Kovrizhin 3, S. Ouvry 1, G. V. Shlyapnikov 1, 4

Physical Review A: Atomic, Molecular and Optical Physics 80 (2009) 063621

We present an analytical solution for the vortex lattice in a rapidly rotating trapped Bose-Einstein condensate (BEC) in the lowest Landau level and discuss deviations from the Thomas-Fermi density profile. This solution is exact in the limit of a large number of vortices and is obtained for the cases of circularly symmetric and narrow channel geometries. The latter is realized when the trapping frequencies in the plane perpendicular to the rotation axis are different from each other and the rotation frequency is equal to the smallest of them. This leads to the cancelation of the trapping potential in the direction of the weaker confinement and makes the system infinitely elongated in this direction. For this case we calculate the phase diagram as a function of the interaction strength and rotation frequency and identify the order of quantum phase transitions between the states with a different number of vortex rows.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
• 3. Theoretical Physics, Oxford University, University of Oxford
• 4. Van der Waals-Zeeman Institute, University of Amsterdam

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• Hall effect in the pinned and sliding charge density wave state of NbSe3

A.A. Sinchenko 1 R.V. Chernikov 1 A.A. Ivanov 1 Pierre Monceau 2 Thierry Crozes 3 S. Brazovskii 4

Journal of Physics: Condensed Matter, Institute of Physics: Hybrid Open Access, 2009, 21 (43), pp.435601

Results of Hall effect measurements are reported both below and above the threshold electric field, E-t, for depinning the low temperature charge density wave (CDW) in NbSe3 in a wide temperature range. At low electric fields, below E-t, we have observed a change in the sign of the Hall voltage at all temperatures lower than T-p2. Comparison between the Hall effect and the magnetoresistance behavior indicates that the n-type conductivity in the low magnetic field range differs qualitatively from the p-type conductivity in the high field range. We demonstrate that at low temperature the CDW motion significantly alters the Hall voltage. These results indicate that, in NbSe3, the CDW in the sliding state interacts essentially with holes. Possible mechanisms of this effect are discussed.

• 1. Moscow Engineering-Physics Institute
• 2. CristElec MagSup
• 3. Nanofab
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• Assessing the impact of transgenerational epigenetic variation on complex traits

Frank Johannes 1, 2, 3, 4 Emmanuelle Porcher 5, 2 Felipe K. Teixeira 6, 7 Vera Colombani-Saliba 5, 2 Matthieu Simon 8 Nicolas Agier 6 Agnès Bulski 1, 7 Juliette Albuisson 1 Fabiana Heredia de Oliveira 1 Pascal Audigier 1 David Bouchez 8 Christine Dillmann 5 Philippe Guerche 9 Frédéric Hospital 10, 3 Vincent Colot 1, 7

PLoS Genetics, Public Library of Science, 2009, 5 (6), Non paginé. <10.1371/journal.pgen.1000530>

Loss or gain of DNA methylation can affect gene expression and is sometimes transmitted across generations. Such epigenetic alterations are thus a possible source of heritable phenotypic variation in the absence of DNA sequence change. However, attempts to assess the prevalence of stable epigenetic variation in natural and experimental populations and to quantify its impact on complex traits have been hampered by the confounding effects of DNA sequence polymorphisms. To overcome this problem as much as possible, two parents with little DNA sequence differences, but contrasting DNA methylation profiles, were used to derive a panel of epigenetic Recombinant Inbred Lines (epiRILs) in the reference plant Arabidopsis thaliana. The epiRILs showed variation and high heritability for flowering time and plant height (~30%), as well as stable inheritance of multiple parental DNA methylation variants (epialleles) over at least eight generations. These findings provide a first rationale to identify epiallelic variants that contribute to heritable variation in complex traits using linkage or association studies. More generally, the demonstration that numerous epialleles across the genome can be stable over many generations in the absence of selection or extensive DNA sequence variation highlights the need to integrate epigenetic information into population genetics studies.

• 1. URGV - Unité de recherche en génomique végétale
• 2. Station de Génétique et d'Amélioration des Plantes UR 254
• 3. Laboratoire de Physique Théorique et Modèles Statistiques UMR 8626
• 4. Groningen Bioinformatics Centre
• 5. GQE - Génétique Quantitative et Evolution (Génétique Végétale)
• 6. UMR 1165, Unité de recherche en Génomique Végétale
• 7. CNRS UMR 8186, Département de Biologie
• 8. UR254 - Unité de Recherche en Génétique et Amélioration des Plantes
• 9. IJPB - Institut Jean-Pierre Bourgin
• 10. GABI - Génétique Animale et Biologie Intégrative

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• Anderson localization of a weakly interacting one-dimensional Bose gas

T. PaulM. AlbertP. Schlagheck 1 P. Leboeuf 2 N. Pavloff 2

Physical Review A, American Physical Society, 2009, 80 (3), 〈10.1103/PhysRevA.80.033615〉

• 1. Institut für Theoretische Physik
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• Archive ouverte HAL – Anderson localization of a weakly interacting one-dimensional Bose gas

T. PaulM. AlbertP. Schlagheck 1 P. Leboeuf 2 N. Pavloff 2

Physical Review A, American Physical Society, 2009, 80 (3), 〈10.1103/PhysRevA.80.033615〉

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