Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

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Séminaire de groupe

Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
Alexandre Lazarescu
jeudi 19 décembre 2013 , 10h15
Salle de séminaire du groupe de Physique Statistique

In this seminar, we consider one of the most popular models of non-equilibrium statistical physics: the Asymmetric Simple Exclusion Process, in which particles jump stochastically on a one-dimensional lattice, between two reservoirs at fixed densities, with the constraint that each site can hold at most one particle at a given time. This model has the mathematical property of being integrable, which makes it a good candidate for exact calculations. What interests us in particular is the current of particles that flows through the system (which is a sign of it being out of equilibrium), and how it fluctuates with time. We will see how, combining calculations from the algebraic Bethe Ansatz, the Macroscopic Fluctuation Theory, and asymptotic direct diagonalisation, we can build the phase diagram for the large deviations of the particle current flowing through this system, and describe the large deviation function of the current as well as the optimal density profiles in each of its five phases. We show that two situations arise : in most phases, the system can be described hydrodynamically, but in one phase, where the current is larger than the limit set by hydrodynamics, the system becomes highly correlated. Keywords: Exclusion process, non-equilibrium statistical physics, large deviations, Bethe Ansatz

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