## Séminaire de Physique Théorique

**Fluctuations of the current in the open ASEP : results from quantum integrability**

Alexandre Lazarescu (KU Leuven, Belgique)

Thursday 12 June 2014 14:00 - Tours - Salle 1180 (Bât E2)

**Résumé :**

The asymmetric simple exclusion process (or ASEP, where particles jump stochastically on a 1D lattice, with hard core repulsion and biased rates) is possibly the most studied model in non-equilibrium statistical mechanics, in part for the reason that it is integrable. Because of the bias in the jumping rates, a net current of particles flows through the system in its stationary state. That current is related to the microscopic irreversibility of the system, and is therefore of particular interest. After introducing the model and a few standard techniques for computing fluctuations in stochastic processes, we will see how one can obtain information on that particle current using the integrability of the model. We will construct a family of commuting transfer matrices with two free parameters, which we will find to be the product of two Q-operators. From algebraic properties of these objects, we can recover the T-Q equations for the open ASEP, and, through functional Bethe Ansatz techniques, obtain the exact satistics of the stationary particle current. Ref. arXiv:1403.6963

**Liens :**