Séminaire du LPTMS: Alexandre Lazarescu


11:30 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405
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On the hydrodynamic behaviour of interacting lattice gases far from equilibrium

Alexandre Lazarescu (Centre de Physique Théorique, École Polytechnique)

Lattice gases are a particularly rich playground to study the large scale emergent behaviour of microscopic models. A few things are known in general for models that are sufficiently close to equilibrium (i.e. with rates close to detailed balance, and where the dynamics is typically diffusive): in particular, the local density of particles behaves autonomously in the macroscopic limit, even at the level of large deviations, and the system can be described through a Langevin equation involving only a few quantities called transport coefficients. As demonstrated in the previous talk, obtaining those coefficients in practice can be quite challenging, but we can usually be confident that they exist.

I will be talking about a situation that is quite different at first sight: systems far from equilibrium, where the dynamics is propagative, and where very little is known in general. The question is then whether one can hope to be able to describe those models with a similar hydrodynamic structure, or if that description breaks down (if, for instance, long-range correlations become relevant). I will present recent results showing that, for a broad class of 1D models with hard-core repulsion but also interactions and space-dependent rates, the answer is yes and no: all those models exhibit a dynamical phase transition between a hydrodynamic regime and a highly correlated one, which can be related to the so-called « third order phase transitions ». The methods involved are quite general and likely to be applicable to many more families of models.

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