Computer simulation of shock waves in the completely asymmetric simple exclusion process

Abstract

We study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average densityρ ₋ (ρ ₊) left (right) of the origin,ρ ₋⩽ρ ₊. The microscopic shock position is identified by introducing a “second-class” particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock positionN(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover$N(t)_{\frown \,}^\smile V \cdot t$, withV=1−ρ ₋−ρ ₊, as predicted, and the dispersion ofN(t), σ²(t), behaves linearly, for not too small values ofρ ₊−ρ ₋, i.e.,$\sigma ^2 (t)_{\frown \,}^\smile S \cdot t$, whereS is equal, up to a scaling factor, to the valueS _WA predicted in the weakly asymmetric case. Forρ ₊=ρ ₋ we find agreement with the conjecture$\sigma ^2 (t)_{\frown \,}^\smile \bar S \cdot t^{4/3}$.