Asymmetric Coupling in Two-Channel Simple Exclusion Processes

TL;DR

This paper investigates two-channel simple exclusion processes with asymmetric inter-channel coupling, revealing complex phase behavior, including seven stationary phases and a novel maximal-current phase, supported by theoretical analysis and Monte Carlo simulations.

Contribution

It introduces an approximate theoretical approach to analyze asymmetric coupling in two-channel exclusion processes, uncovering new phase phenomena not seen in symmetric systems.

Findings

Seven stationary phases identified under asymmetric coupling.

Discovery of a new maximal-current phase with a domain wall.

Excellent agreement between theory and Monte Carlo simulations.

Abstract

Simple exclusion processes for particles moving along two parallel lattices and jumping between them are theoretically investigated for asymmetric rates of transition between the channels. An approximate theoretical approach, that describes the particle dynamics exactly in any vertical cluster of two parallel sites and neglects the correlations between the different vertical clusters, is applied to calculate stationary-state density profiles, currents and phase diagrams. Surprisingly, it is found that asymmetry in the coupling between the channels leads to a very complex phase behavior that is very different from two-channel simple exclusion processes with symmetric coupling. There are seven stationary-state phases in the simple exclusion processes with asymmetric transition rates between the channels, in contrast to three phases found for the systems with symmetric coupling. In addition, a new maximal-current phase with a domain wall in the middle of the lattices, that has no analogs in other exclusion processes, is observed. Although the explicit calculations are presented only for the case of full asymmetry, when the particles can only jump between the channels in one direction, the properties of two-channel simple exclusion systems with general asymmetry are also discussed. Theoretical predictions are in excellent agreement with extensive computer Monte Carlo simulations.