title: 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-|t|/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 v{max}=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 parameter τ corresponds to the integrated autocorrelation time, which plays a fundamental role in quantifying the statistical errors in Monte Carlo simulations of these models.
authors.affiliation: Department of Mathematics and Statistics, The University of Melbourne, Victoria, Australia. jdgier@unimelb.edu.au
authors.forename: Jan
authors.initials: J
authors.lastname: de Gier
authors.forename: Timothy M
authors.initials: TM
authors.lastname: Garoni
authors.forename: Zongzheng
authors.initials: Z
authors.lastname: Zhou