Asymmetric simple exclusion process with periodic boundary driving

TL;DR

This paper analyzes the ASEP with periodic boundary driving, revealing a universal sawtooth density profile shape and exploring boundary effects through analytical, numerical, and simulation methods.

Contribution

It provides an analytical description of the time-periodic density profile and compares different approaches to determine boundary densities in driven diffusive systems.

Findings

Density profile is sawtooth-shaped and time-periodic.

Stationary state governed by effective boundary densities.

Numerical and mean field methods agree with hydrodynamic limit.

Abstract

We consider the asymmetric simple exclusion process (ASEP) on a semi-infinite chain which is coupled at the end to a reservoir with a particle density that changes periodically in time. It is shown that the density profile assumes a time-periodic sawtooth-like shape. This shape does not depend on initial conditions and is found analytically in the hydrodynamic limit. In a finite system, the stationary state is shown to be governed by effective boundary densities and the extremal flux principle. Effective boundary densities are determined numerically via Monte Carlo simulations and compared with those given by mean field approach and numerical integration of the hydrodynamic limit equation which is the Burgers equation. Our results extend straightforwardly beyond the ASEP to a wide class of driven diffusive systems with one conserved particle species.