Modelling one-dimensional driven diffusive systems by the Zero-Range Process

TL;DR

This paper extends the Zero-Range Process correspondence to two-species driven systems with unequal densities, introducing numerical and analytical methods to evaluate currents and analyze phase separation.

Contribution

It develops a generalized framework linking two-species driven models to the Zero-Range Process for unequal densities, including a new numerical method and a domain dynamics model.

Findings

Validated the numerical method for current evaluation

Derived phase separation transition line for a specific model

Extended the theoretical framework to non-equal densities

Abstract

The recently introduced correspondence between one-dimensional two-species driven models and the Zero-Range Process is extended to study the case where the densities of the two species need not be equal. The correspondence is formulated through the length dependence of the current emitted from a particle domain. A direct numerical method for evaluating this current is introduced, and used to test the assumptions underlying this approach. In addition, a model for isolated domain dynamics is introduced, which provides a simple way to calculate the current also for the non-equal density case. This approach is demonstrated and applied to a particular two-species model, where a phase separation transition line is calculated.