Universality in the symmetric exclusion process (Vol. 44 No. 6)

A system connected to two sources of heat or particles reaches, in the long time limit, a non-equilibrium steady state characterized by a non-vanishing and fluctuating current. Its study is an active topic in both classical and quantum systems. A relevant observable is the number Qt of particles flowing through the system during a time t. It can be calculated for simple models such as the symmetric simple exclusion process (SSEP), which describes two reservoirs at fixed densities connected by an L-site chain on which particles diffuse with a same site hard core repulsion. The corresponding cumulants of Qt are exactly known in one dimension and they coincide with those computed for the transport of free fermions through a mesoscopic conductor. We have generalized these results to arbitrary large but finite d-dimensional domains or graphs. Our numerical results indicate that, for large enough lattices and contacts to the reservoirs, the ratios of the cumulants of Qt take universal values, independent of the domain dimension and shape.

E. Akkermans, T. Bodineau, B. Derrida and O. Shpielberg, ‘Universal current fluctuations in the symmetric exclusion process and other diffusive systems, EPL, 103, 20001 (2013)