Weakly coupled, antiparallel, totally asymmetric simple exclusion processes

TL;DR

This paper analyzes a two-lane asymmetric exclusion process with particles moving in opposite directions, revealing complex phase behavior including localized shocks, phase transitions, and shock dynamics influenced by lane interactions.

Contribution

It introduces a novel model of coupled exclusion processes with inverse rate lane changes, providing analytical and numerical phase diagrams and uncovering new shock phenomena.

Findings

Identification of phases with localized shocks in one lane

Discovery of a discontinuous phase transition with delocalized shocks

Analysis of shock confinement due to asymmetric lane change

Abstract

We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely proportional to the length of the system. Stationary density profiles are determined and the phase diagram of the model is constructed in the hydrodynamic limit, by solving the differential equations describing the steady state of the system, analytically for vanishing total current and numerically for nonzero total current. The system possesses phases with a localized shock in the density profile in one of the lanes, similarly to exclusion processes endowed with nonconserving kinetics in the bulk. Besides, the system undergoes a discontinuous phase transition, where coherently moving delocalized shocks emerge in both lanes and the fluctuation of the global density is described by an unbiased random walk. This phenomenon is analogous to the phase coexistence observed at the coexistence line of the totally asymmetric simple exclusion process, however, as a consequence of the interaction between lanes, the density profiles are deformed and in the case of asymmetric lane change, the motion of the shocks is confined to a limited domain.