Boundary driven zero-range processes in random media

TL;DR

This paper investigates the stationary states and particle dynamics of boundary driven zero-range processes in disordered media, revealing how strong disorder influences system behavior and particle trajectories.

Contribution

It introduces analysis of zero-range processes in random media with quenched disorder, highlighting the effects of boundary driving and strong disorder on stationary states and particle motion.

Findings

Stationary states are trivial without boundary drive in symmetric models.

Strong disorder leads to fugacity profiles governed by $ ext{alpha}$-stable subordinators.

Expectations of tagged particle positions are computed for various routes.

Abstract

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.