Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas

TL;DR

This paper combines phenomenological theories and Monte-Carlo simulations to analyze the dynamics of the asymmetric exclusion process, revealing detailed behaviors of density fluctuations and domain wall motion across different phases.

Contribution

It integrates domain wall theory with Boltzmann-Langevin approach to provide a comprehensive understanding of driven lattice gas dynamics at phase boundaries.

Findings

Time scale separation between local density fluctuations and domain wall motion.

Correlation functions and power spectra data across the full parameter range.

Qualitative agreement between theory and Monte-Carlo simulations.

Abstract

We study the dynamics of the totally asymmetric exclusion process with open boundaries by phenomenological theories complemented by extensive Monte-Carlo simulations. Upon combining domain wall theory with a kinetic approach known as Boltzmann-Langevin theory we are able to give a complete qualitative picture of the dynamics in the low and high density regime and at the corresponding phase boundary. At the coexistence line between high and low density phases we observe a time scale separation between local density fluctuations and collective domain wall motion, which are well accounted for by the Boltzmann-Langevin and domain wall theory, respectively. We present Monte-Carlo data for the correlation functions and power spectra in the full parameter range of the model.