Parallel Coupling of Symmetric and Asymmetric Exclusion Processes

TL;DR

This paper studies a coupled system of symmetric and asymmetric exclusion processes, revealing how strong inter-channel couplings influence the system's phase behavior and effectively transform the dynamics, supported by exact solutions, approximations, and simulations.

Contribution

It introduces a vertical cluster mean-field method for intermediate couplings and provides exact solutions for strong couplings in a coupled symmetric-asymmetric exclusion system.

Findings

Strong symmetric couplings lead to an effective PASEP with similar channel properties.

Strong asymmetric couplings produce an effective TASEP with nonzero flux in the asymmetric channel.

Three stationary phases are identified, with phase boundaries depending on coupling strength and symmetry.

Abstract

A system consisting of two parallel coupled channels where particles in one of them follow the rules of totally asymmetric exclusion processes (TASEP) and in another one move as in symmetric simple exclusion processes (SSEP) is investigated theoretically. Particles interact with each other via hard-core exclusion potential, and in the asymmetric channel they can only hop in one direction, while on the symmetric lattice particles jump in both directions with equal probabilities. Inter-channel transitions are also allowed at every site of both lattices. Stationary state properties of the system are solved exactly in the limit of strong couplings between the channels. It is shown that strong symmetric couplings between totally asymmetric and symmetric channels lead to an effective partially asymmetric simple exclusion process (PASEP) and properties of both channels become almost identical. However, strong asymmetric couplings between symmetric and asymmetric channels yield an effective TASEP with nonzero particle flux in the asymmetric channel and zero flux on the symmetric lattice. For intermediate strength of couplings between the lattices a vertical cluster mean-field method is developed. This approximate approach treats exactly particle dynamics during the vertical transitions between the channels and it neglects the correlations along the channels. Our calculations show that in all cases there are three stationary phases defined by particle dynamics at entrances, at exits or in the bulk of the system, while phase boundaries depend on the strength and symmetry of couplings between the channels. Extensive Monte Carlo computer simulations strongly support our theoretical predictions.