Zero-range processes with saturated condensation: the steady state and dynamics

TL;DR

This paper investigates a class of zero-range processes where saturated condensation occurs instead of real-space condensation, analyzing the steady state conditions and the dynamics of relaxation through theoretical methods.

Contribution

It introduces the concept of saturated condensation in zero-range processes and characterizes the conditions and dynamics leading to this state.

Findings

Saturated condensation replaces real-space condensation in certain zero-range processes.

Two-stage relaxation dynamics identified: rapid condensate growth followed by slow evaporation and condensation.

Theoretical analysis combines mean-field, first-passage, and fluctuation-dissipation approaches.

Abstract

We study a class of zero-range processes in which the real-space condensation phenomenon does not occur and is replaced by a saturated condensation: that is, an extensive number of finite-size "condensates" in the steady state. We determine the conditions under which this occurs, and investigate the dynamics of relaxation to the steady state. We identify two stages: a rapid initial growth of condensates followed by a slow process of activated evaporation and condensation. We analyze these nonequilibrium dynamics with a combination of meanfield approximations, first-passage time calculations and a fluctuation-dissipation type approach.