Canonical Analysis of Condensation in Factorised Steady State

TL;DR

This paper analyzes the structure and nature of condensation transitions in mass transport models with factorized steady states, revealing two distinct regimes of condensate behavior and providing exact asymptotic results.

Contribution

It offers a detailed canonical ensemble analysis of condensation, identifying two regimes of condensate fluctuations and shapes, and extends understanding beyond grand canonical approaches.

Findings

Identifies gaussian and non-gaussian condensate regimes

Derives asymptotically exact shape and size of condensates

Discovers cases with pseudocondensates at superextensive densities

Abstract

We study the phenomenon of real space condensation in the steady state of a class of mass transport models where the steady state factorises. The grand canonical ensemble may be used to derive the criterion for the occurrence of a condensation transition but does not shed light on the nature of the condensate. Here, within the canonical ensemble, we analyse the condensation transition and the structure of the condensate, determining the precise shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is gaussian distributed and the particle number fluctuations scale normally as $L^{1/2}$ where $L$ is the system size, and a second regime where the particle number fluctuations become anomalously large and the condensate peak is non-gaussian. Our results are asymptotically exact and can also be interpreted within the framework of sums of random variables. We further analyse two additional cases: one where the condensation transition is somewhat different from the usual second order phase transition and one where there is no true condensation transition but instead a pseudocondensate appears at superextensive densities.