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

TL;DR

This study uses Monte Carlo simulations to analyze autocorrelation functions in the Nagel-Schreckenberg model, revealing a linear decay pattern and providing insights into the autocorrelation time's dependence on system parameters.

Contribution

It demonstrates that autocorrelation functions in the model decay linearly with a finite support and identifies the exact dependence of autocorrelation time on system parameters in the TASEP limit.

Findings

Autocorrelation functions decay as 1-|t|/tau with finite support.

Autocorrelation time tau is proportional to system size divided by a constant c.

Exact dependence of c on input, output, and hopping rates in the TASEP limit.

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 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.