韩国裸舞

On the hydrodynamic behaviour of interacting lattice gases far from equilibrium

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 local Langevin equation involving only a few quantities called transport coefficients. 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 examine a class of 1D models based on the Asymmetric Simple Exclusion Process (ASEP), a well-known and well-studied toy model with hard-core repulsion, which happens to be exactly solvable through quantum integrability techniques. Those models, where I add interactions and space-dependent rates (thus making them non-integrable), all exhibit a dynamical phase transition between a hydrodynamic regime similar to the equilibrium case and a highly correlated regime where locality is broken. The methods involved are quite general and likely to be applicable to many more families of models.