Séminaire commun LPT/LPTMS 2011-2012

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  Jeudi 29 Mars 2012 à 14h, Salle 201, bât. 100A (LPTMS)

Olga Dimitrova (LPTMS)

Zero temperature criticality in the Gaussian random bond Ising model on a square lattice

The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion and analysis of continuation of the high-temperature series. At low temperatures the specific heat reveals a zero temperature criticality described by the power law $C\propto T^1+\alpha$, with $\alpha= 0.58(9)$, the result confirmed independently by counting many-body states in finite size samples. Interpretation of the free energy in terms of droplet excitations gives the density of two-level states, that follows a novel power law $\rho(\epsilon)\propto \epsilon^\alpha$ at low energies.

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  Jeudi 15 Mars 2012 à 14h, Salle 201, bât. 100A (LPTMS)

Gregory Berkolaiko (Texas A&M University)

Universality in chaotic quantum transport : the concordance between random matrix and semiclassical theories

Electronic transport through chaotic quantum dots exhibits universal, system independent properties which are consistent with random matrix theory. The observable quantities can be expressed, via the semiclassical approximation, as sums over the classical scattering trajectories. Correlations between such trajectories are organized diagrammatically and have been shown to yield universal answers for some observables.

We develop a general combinatorial treatment of the semiclassical diagrams by casting them as unicellular maps (graphs embedded on surfaces) and relating them to factorizations of permutations. The expansion of transport quantities in inverse channel number corresponds to a genus expansion of the combinatorial generating function. Taking previously calculated answers (Heusler et al, 2006) for the contribution of a given diagram, we prove agreement between the semiclassical and random matrix approaches to moments of the transmission amplitudes. The proof covers all orders, all moments (including nonlinear), and systems with or without time reversal symmetry. It explains the mathematics behind the applicability of random matrix theory to chaotic quantum transport. The streamlined calculation could also pave the way for inclusion of non-universal effects.

Based on joint work with Jack Kuipers (Regensburg)

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  Jeudi 8 Mars 2012 à 14h, Salle 114, bât. 210 (LPT)

Masaharu Isobe (Nagoya Institute of Technology)

Higher Order Parameters for Establishing Transient Crystals

The long slow decaying potential part of the stress autocorrelation function has been called the “molasses tail” to distinguish it from the hydrodynamic origin of the long time tail in the velocity autocorrelation functions and to emphasize its relation to highly viscous glassy state. We are investigating the molasses tail in dense hard core fluids by using extensive Event-Driven MD simulation through the orientational autocorrelation functions[1, 2]. Near the fluid-solid phase transition, there exist three regimes in the relaxation of the pair orientational autocorrelation function, namely the kinetic, molasses(stretched exponential), and diffusional power decay. The most striking observation through the bond orientatinal order parameter is the dramatic increase of the transient nuclei cluster size near the freezing density[2]. We are now improving the alternative general methods based on the autocorrelation functions of higher order parameters even for quadruplet contributions (i.e. 8 point-correlation) to establish the transient nuclei, which are composed of a few hundred hard particles in dense liquid system [3].

[1] M. Isobe and B. J. Alder, Mol. Phys. 107, 609 (2009).

[2] M. Isobe and B. J. Alder, Prog. Theor. Phys. Suppl. 184, 437 (2010).

[3] M. Isobe and B. J. Alder, in preparation.

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  Jeudi 16 Février 2012 à 14h, Salle 201, bât. 100A (LPTMS)

Sylvie Méléard (Centre de Mathématiques Appliquées, Ecole Polytechnique)

Modélisation aléatoire des dynamiques adaptatives pour des populations sexuées

Dans un travail commun avec Pierre Collet (CPHT, Ecole Polytechnique) et Hans Metz (University of Leiden) nous introduisons un modèle probabiliste qui décrit la dynamique temporelle d’une population sexuée et prend en compte les événements de reproduction et de mort de chaque individu. De plus le modèle intègre les lois mendéliennes de la reproduction avec sélection et de possibles mutations alléliques et également la compétition entre les individus à travers le partage de ressources limitées. Nous montrons que sous des hypothèses de grande population, mutations rares et dans une longue échelle de temps, le processus converge vers un processus de saut pur qui décrit l’évolution entre des équilibres du système de Lotka-Volterra sous-jacent. Si de plus nous supposons que les amplitudes de mutations sont petites, nous montrons que la dynamique se rapproche de celle de l’équation canonique des dynamiques adaptatives pour les populations asexuées.

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  Jeudi 9 Février 2012 à 14h, Salle 114, bât. 210 (LPT)

Thierry Bodineau (DMA - ENS)

Corrélations à longue portée dans des systèmes hors équilibre

Les systèmes maintenus hors équilibre ont, en général, des corrélations à longue portée dans l’état stationnaire. Nous décrirons quelques exemples de dynamiques stochastiques où ce type de corrélations peut être calculé (exclusion symétrique avec batterie, modèle ABC) et discuterons les singularités de ces corrélations à l’approche de la transition de phase.

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  Mercredi 25 Janvier 2012 à 14h, Salle 201, bât. 100A (LPTMS)

Nicolas Macris (ETH Zurich)

Bethe free energy of low-density error correcting codes : rigorous methods and results

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  Jeudi 19 Janvier 2012 à 14h, Salle 114, bât. 210 (LPT)

SEMINAIRE ANNULE

Tomoko Mizuguchi (Unité Matériaux et Transformations, Université Lille 1)

The role of the attractive part of the interaction potential in the glass forming ability

The glass-forming ability of simple Lennard-Jones liquids has been investigated from Molecular Dynamics Simulations. Three models have been studied that only differ from the attractive part of the interparticle potential. The resistance to crystallization from the liquid state has been studied based on calculations of the surface tension and the differences in the Gibbs free energy between the amorphous and crystalline phases. The role of the softness of the interaction potential in the glass forming ability is discussed in the framework of the classical nucleation theory.

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  Jeudi 15 Décembre 2011 à 14h, Salle 114, bât. 210 (LPT)

Chikashi Arita (IPhT, CEA Saclay)

Queueing Process with Exclusion

The queueing process is one of the simplest model with injection and extraction of particles. When we (pedestrians) make a queue, we can proceed if there is a space in front of us. However this excluded-volume effect of queues is neglected in the usual queueing process. Recently the speaker introduced a simple extension of the queueing process with excluded-volume effect ("exclusive queueing process", EQP) by imposing a new boundary condition on the asymmetric exclusion process. The usual queueing process converges if the injection rate is smaller than the extraction rate. On the other hand the injection rate cannot be larger than the maximal current of the asymmetric exclusion process for convergence of the EQP, i.e. "the queue itself is a bottleneck". This talk is based on the following works.

[1] CA, Physical Review E (2009)

[2] CA and D Yanagisawa, Journal of Statistical Physics (2010)

[3] CA and A Schadschneider, Physical Review E (2011)

[4] CA and A Schadschneider, arXiv:1109.0425v1

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  Jeudi 8 Décembre 2011 à 14h, Salle 201, bât. 100A (LPTMS)

Olga Valba (LPTMS)

On two morphological transitions in secondary structure of random RNA-like polymers

We have shown that there is a transition in the structure of random RNA-like heteropolymers with change of the number of types of monomers, c. For c<=4 the fraction of "active’’ (connected) nucleotides tends to 1 as the length of the chain goes to infinity, signaling the formation of a "perfect’’ secondary structure without gaps. In turn, for c>4 the fraction of "active" monomers tends to some self-averaged value, meaning that gaps are necessarily presented in structure. Such a critical behavior allows one to speculate about exclusivity of a c=4-letter alphabet used in natural RNAs.

Another topological transition is observed in the following model (random interval model). We have considered a polymer with random intervals between neighboring monomers. The interaction energy is taken as a convex function of distance between monomers. Two distributions of intervals are considered : Gaussian and power law. The ground state structure of the polymer is obtained via some transport optimization problem. It has been observed that with change of the parameters of the distribution, the polymer topology undergoes essential modification from sequential distribution of optimal pairings to the hierarchical RNA-like one.

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  Jeudi 24 Novembre 2011 à 14h, Salle 114, bât. 210 (LPT)

David Mukamel (Department of Physics of Complex Systems, Weizmann Institute)

Density large deviations of nonconderving driven ABC model

The effect of particle-nonconserving processes on the steady state of driven diffusive systems will be discussed. It is shown that in the limit of slow nonconserving processes the large deviations function of the overall density can computed given known properties of the steady of the conserving model. This enables one to compute phase diagrams and to define a nonequilibrium chemical potential which unlike the equilibrium case, is dynamics dependent and can show negative compressibility. Correspondence with equilibrium systems with long-range interactions is pointed out. The approach is demonstrated for the ABC model, a driven model exhibiting phase separation in one dimension.

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  Jeudi 17 Novembre 2011 à 14h, Salle 201, bât. 100A (LPTMS)

Thierry Mora (LPS - ENS)

Emergent phenomena in biology : proteins, bird flocks and microbial colonies

Biological systems with many players (or degrees of freedom) often display emergent collective behaviour---their overall properties cannot be explained by just the sum of individual contributions. Sometimes, these collective behaviours are reminiscent of critical phenomena in physics, with the observation of power laws, the divergence of characteristic length scales, etc. Statistical mechanics offers a useful tool for describing such phenomena. I will show how well-known statistical mechanics models can be explicitly mapped onto biological data and used to predict their collective properties on three examples, two of which exhibit critical properties : a disordered Potts model for analysing the diversity of immune receptor proteins, a Heisenberg model for explaining flight alignment in flocks of birds, and a simple diffusion model for describing the management of a public good (siderophores) in a growing population of bacteria (P. aeruginosa).

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  Jeudi 27 Octobre 2011 à 14h, Salle 114, bât. 210 (LPT)

Simona Cocco (LPS - ENS)

Une expansion adaptative en clusters pour le problème inverse d’Ising

Je présenterai une méthode pour retrouver les interactions et champs d’un modèle d’Ising étant donne les corrélations à un et deux points. La méthode consiste à construire et sélectionner des clusters de spins spécifiques, en se basant sur leur contributions à l’entropie du modèle d’Ising. Je discuterai les propriétés de cette expansion en clusters sur des modèles simples et des données biologiques.

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  Jeudi 13 Octobre 2011 à 14h, Salle 201, bât. 100A (LPTMS)

Alfredo Ozorio de Almeida (CBPF — Centro Brasileiro de Pesquisas Fisicas — Rio de Janeiro)

An initial value representation for the quantum Loschmidt echo

Initial value representations (IVR) have been an attractive practical alternative to traditional semiclassical approximations for the quantum evolution, even in cases where their justification is not clear. This is because they bypass the search for particular appropriate classical trajectories and the need for special treatment near caustics. The `defasing representation’ proposed by Vanicek is a case in point. It deals with a combination of nearly identical forward and backward motions, in strict analogy to the (classical) Loschmidt echo, by adding a simple phase to each classical trajectory for all arguments of the Wigner function. It will be shown that this is only a small restriction on a slightly more elaborate IVR, appropriately derived from standard semiclassical approximations for the evolution of the Wigner function.

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