Stationary state of a zero-range process corresponding to multifractal one-particle distribution

TL;DR

This paper studies a zero-range process with a multifractal one-particle distribution, revealing condensation phenomena and scaling behaviors influenced by disorder strength, supported by branching process models.

Contribution

It introduces a zero-range process model with a multifractal stationary distribution and analyzes condensation and scaling properties in large systems.

Findings

Particles condense at the site with highest measure

Condensate size scales algebraically with system size

Branching process models replicate multifractal properties

Abstract

We investigate a zero-range process where the underlying one-particle stationary distribution has multifractality. The multiparticle stationary probability measure can be written in a factorized form. If the number of the particles is sufficiently large, a great part of the particles condense at the site with the highest measure of the one-particle problem. The number of the particles out of the condensate scales algebraically with the system size and the exponent depends on the strength of the disorder. These results can be well reproduced by a branching process, with similar multifractal property.