Autocorrelations in the totally asymmetric simple exclusion process and Nagel-Schreckenberg model

Abstract

We study via Monte Carlo simulation the dynamics of the Nagel-Schreckenberg model on a finite system of length L with open boundary conditions and parallel updates. We find numerically that in both the high and low density regimes the autocorrelation function of the system density behaves like 1- ΙtΙ /τ with a finite support [-τ,τ]. This is in contrast to the usual exponential decay typical of equilibrium systems. Furthermore, our results suggest that in fact τ=L/c, and in the special case of maximum velocity vmax =1 (corresponding to the totally asymmetric simple exclusion process) we can identify the exact dependence of c on the input, output and hopping rates. We also emphasize that the p..