TASEP on a ring with internal degrees of freedom

TL;DR

This paper analyzes a TASEP model with internal degrees of freedom on a ring, deriving exact steady state weights and correlations, revealing how internal state-dependent hopping rates induce non-trivial correlations.

Contribution

It introduces a matrix product solution for a TASEP with internal states and maps it to a zero range process, providing exact correlation calculations.

Findings

Steady state weights expressed in matrix product form

Exact spatial correlation functions derived

Unequal hopping rates cause non-trivial correlations

Abstract

A totally asymmetric exclusion process on a ring with $\nu$ non-conserved internal degrees of freedom, where particles hop forward with a rate that depends on their internal state, has been studied. We show, using a mapping of the model to a zero range process with $\nu$ different kinds of boxes, that steady state weights can be written in a matrix product form and calculate the spatial correlations exactly. A comparison of the model with an equivalent conserved system reveals that unequal hopping rates of particles belonging to different internal states is responsible for the non-trivial correlations.