Two-Channel Totally Asymmetric Simple Exclusion Processes

TL;DR

This paper analyzes a two-channel totally asymmetric simple exclusion process, deriving exact solutions for strong coupling and an approximate theory for intermediate coupling, supported by Monte Carlo simulations, revealing phase behavior dependent on inter-channel coupling.

Contribution

It introduces an exact solution for strong coupling and a new approximate model for intermediate coupling in two-channel exclusion processes, expanding understanding of phase behavior.

Findings

Exact solutions for strong coupling case.

Approximate theory for intermediate coupling.

Monte Carlo simulations confirm theoretical predictions.

Abstract

Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase diagram are calculated exactly by mapping the system into an effective one-channel totally asymmetric exclusion model. For intermediate couplings, a simple approximate theory, that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters, is developed. It is found that, similarly to the case of one-channel totally asymmetric simple exclusion processes, there are three stationary state phases, although the phase boundaries and stationary properties strongly depend on inter-channel coupling. An extensive computer Monte Carlo simulations fully support the theoretical predictions.