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 Q_t 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 Q_t 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 Q_t take universal values, independent of the domain dimension and shape.