Spontaneous pulsing states in an active particle system

TL;DR

This paper investigates a two-lane exclusion process that exhibits a non-equilibrium pulsing phase characterized by density oscillations and a phase transition driven by particle injection and lane-changing rates, supported by analytical and mean-field analysis.

Contribution

It introduces a novel two-lane model showing a pulsing phase with analytical predictions and stability analysis, expanding understanding of non-equilibrium phase transitions.

Findings

Identification of a phase transition from low density to pulsing phase.

Analytical prediction of density profiles in the low density phase.

Observation of density oscillations caused by front movement.

Abstract

We study a two-lane two-species exclusion process inspired by Lin et al. (C. Lin et al. J. Stat. Mech., 2011), that exhibits a non-equilibrium pulsing phase. Particles move on two parallel one-dimensional tracks, with one open and one reflecting boundary. The particle type defines the hopping direction. When only particles hopping towards the open end are allowed to change lane, the system exhibits a phase transition from a low density phase to a pulsing phase depending on the ratio between particle injection and type-changing rate. This phase transition can be observed in the stochastic model as well as in a mean-field description. In the low density phase, the density profile can be predicted analytically. The pulsing phase is characterised by a fast filling of the system and - once filled - by a slowly backwards moving front separating a decreasing dense region and an expanding low density region. The hopping of the front on the discrete lattice is found to create density oscillations, both, in time and space. By means of a stability analysis we can predict the structure of the dense region during the emptying process, characterised by exponentially damped perturbations, both at the open end and near the moving front.