Domain wall theory and non-stationarity in driven flow with exclusion

TL;DR

This paper investigates the non-stationary behavior of the asymmetric simple exclusion process using domain-wall theory and simulations, highlighting the importance of fluctuations for accurate predictions in uniform and staggered chains.

Contribution

It demonstrates the effectiveness of domain-wall theory in capturing non-stationary dynamics and phase diagram features, improving upon mean-field predictions for exclusion processes.

Findings

Domain-wall theory aligns well with simulations for uniform chains.

Fluctuations are crucial for accurate non-stationary predictions.

Approximate agreement with phase diagram features in staggered chains.

Abstract

We study the dynamical evolution toward steady state of the stochastic non-equilibrium model known as totally asymmetric simple exclusion process, in both uniform and non-uniform (staggered) one-dimensional systems with open boundaries. Domain-wall theory and numerical simulations are used and, where pertinent, their results are compared to existing mean-field predictions and exact solutions where available. For uniform chains we find that the inclusion of fluctuations inherent to the domain-wall formulation plays a crucial role in providing good agreement with simulations, which is severely lacking in the corresponding mean-field predictions. For alternating-bond chains the domain-wall predictions for the features of the phase diagram in the parameter space of injection and ejection rates turn out to be realized only in an incipient and quantitatively approximate way. Nevertheless, significant quantitative agreement can be found between several additional domain-wall theory predictions and numerics.