Canonical analysis of condensation in factorised steady states

MR Evans*, SN Majumdar, RKP Zia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)357-390
Number of pages34
JournalJournal of Statistical Physics
Volume123
Issue number2
DOIs
Publication statusPublished - Apr 2006

Keywords

  • stochastic processes
  • zero-range process
  • factorised steady states
  • condensation transition
  • ZERO-RANGE PROCESS
  • STATISTICAL-MECHANICS
  • PHASE-TRANSITIONS
  • STOCHASTIC-MODEL
  • LATTICE-GAS
  • DYNAMICS
  • SYSTEMS
  • STATIONARY
  • BREAKING
  • RING

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