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

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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 /tau with a finite support [-tau,tau]. This is in contrast to the usual exponential decay typical of equilibrium systems. Furthermore, our results suggest that in fact tau=L/c, and in the special case of maximum velocity epsilon(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 tau corresponds to the integrated autocorrelation time, which plays a fundamental role in quantifying the statistical errors in Monte Carlo simulations of these models
Original languageEnglish
Pages (from-to)021107-1 - 021107-7
Number of pages7
JournalPhysical Review E
Volume82
Issue number1
DOIs
Publication statusPublished - 2010
Externally publishedYes

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