Condensate formation in a zero-range process with random site capacities

TL;DR

This paper investigates how quenched disorder with random site capacities influences condensate formation in the zero-range process, revealing conditions for condensation and the impact of disorder on condensate localization and critical density.

Contribution

It provides an exact characterization of condensate formation conditions in a disordered ZRP with finite capacities, extending understanding of disorder effects in interacting particle systems.

Findings

Condensate can relocate on sites with largest capacities.

Critical density distribution follows Gaussian or Levy-stable laws.

Disorder influences both the location and the critical parameters of condensation.

Abstract

We study the effect of quenched disorder on the zero-range process (ZRP), a system of interacting particles undergoing biased hopping on a one-dimensional periodic lattice, with the disorder entering through random capacities of sites. In the usual ZRP, sites can accommodate an arbitrary number of particles, and for a class of hopping rates and high enough density, the steady state exhibits a condensate which holds a finite fraction of the total number of particles. The sites of the disordered zero-range process considered here have finite capacities chosen randomly from the Pareto distribution. From the exact steady state measure of the model, we identify the conditions for condensate formation, in terms of parameters that involve both interactions (through the hop rates) and randomness (through the distribution of the site capacities). Our predictions are supported by results obtained from a direct numerical sampling of the steady state and from Monte Carlo simulations. Our study reveals that for a given realization of disorder, the condensate can relocate on the subset of sites with largest capacities. We also study sample-to-sample variation of the critical density required to observe condensation, and show that the corresponding distribution obeys scaling, and has a Gaussian or a Levy-stable form depending on the values of the relevant parameters.