Computer Simulation of Shock Waves in the Completely Asymmetric Simple Exclusion Process

We study the evolution of the completely asymmetric simple exclusion process in one dimension, for initial configurations corresponding to average density p_ (p+) left (right) of the origin, p_-< p +. The microscopic shock position is identified by introducing a "second class" particle. Results indicate that the shock profile is stable, and the distribution around the shock position N(t) tends, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover the dispersion behaves linearly in time, for not too small values of the density difference.