Hydrodynamics in a condensation regime: the disordered asymmetric zero-range process

TL;DR

This paper investigates the hydrodynamic behavior of a disordered asymmetric zero-range process, establishing a scalar conservation law that describes the macroscopic particle density evolution, including the critical density domain.

Contribution

It provides the first hydrodynamic limit for disordered asymmetric zero-range processes with general jump rates and site disorder, extending previous models.

Findings

Hydrodynamic limit characterized by a scalar conservation law.

Flux remains constant above critical density.

Results hold under suitable averaging properties of the environment.

Abstract

We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant.