Condensation in randomly perturbed zero-range processes

TL;DR

This paper investigates how small perturbations in zero-range processes affect condensation phenomena, providing rigorous results and simulations that clarify the phase diagram and finite system relevance.

Contribution

It offers rigorous analysis of finite critical density and free energy in perturbed zero-range processes, expanding understanding of phase transitions under noise.

Findings

Perturbations prevent condensation in extended parameter ranges.

Finite critical density and free energy are rigorously characterized.

Simulation data supports theoretical predictions and highlights finite system effects.

Abstract

The zero-range process is a stochastic interacting particle system that exhibits a condensation transition under certain conditions on the dynamics. It has recently been found that a small perturbation of a generic class of jump rates leads to a drastic change of the phase diagram and prevents condensation in an extended parameter range. We complement this study with rigorous results on a finite critical density and quenched free energy in the thermodynamic limit, as well as quantitative heuristic results for small and large noise which are supported by detailed simulation data. While our new results support the initial findings, they also shed new light on the actual (limited) relevance in large finite systems, which we discuss via fundamental diagrams obtained from exact numerics for finite systems.