Space-time phase transitions in the totally asymmetric simple exclusion process

Abstract

One can drive a system away from equilibrium by bringing it in contact with reservoirs at a different temperature or chemical potential; as a result, heat or particle currents will develop. Recently, the interest in the fluctuations of these currents has increased considerably, both from a theoretical and an experimental point of view. We studied current fluctuations in the Totally Assymetric Simple Exclusion Process(TASEP), which consists of a one-dimensional lattice in which each site is either empty or occupied by at most one particle. The particles enter the lattice with rate α, and exit the lattice with rate β, provided these moves are allowed by the exclusion statistics. In our work, the current is then taken to be equal to the total number of particles that has passed through all bonds up to a certain time. Using a powerful numerically exact technique called the Density Matrix Renormalization Group (DMRG), we were able to obtain results for the first three cumulants of the current and their time dependence in the various phases of the TASEP (determined by the values of α and β). Furthermore, by studying ensenbles of histories weighted by an exponential function of the current, we found that the TASEP displays a space‐time phase transition.