Nonequilibrium statistical mechanics of the zero-range process and related models

MR Evans*, T Hanney

*Corresponding author for this work

Research output: Contribution to journalLiterature reviewpeer-review

Abstract

We review recent progress on the zero-range process, a model of interacting particles which hop between the sites of a lattice with rates that depend on the occupancy of the departure site. We discuss several applications which have stimulated interest in the model such as shaken granular gases and network dynamics; we also discuss how the model may be used as a coarse-grained description of driven phase-separating systems. A useful property of the zero-range process is that the steady state has a factorized form. We show how this form enables one to analyse in detail condensation transitions, wherein a finite fraction of particles accumulate at a single site. We review condensation transitions in homogeneous and heterogeneous systems and also summarize recent progress in understanding the dynamics of condensation. We then turn to several generalizations which also, under certain specified conditions, share the property of a factorized steady state. These include several species of particles; hop rates which depend on both the departure and the destination sites; continuous masses; parallel discrete-time updating; non-conservation of particles and sites.

Original languageEnglish
Pages (from-to)R195-R240
Number of pages46
JournalJournal of Physics A: Mathematical and General
Volume38
Issue number19
DOIs
Publication statusPublished - 13 May 2005

Keywords

  • ATTRACTIVE PARTICLE-SYSTEMS
  • DISORDERED EXCLUSION MODELS
  • BOSE-EINSTEIN CONDENSATION
  • DRIVEN DIFFUSIVE SYSTEMS
  • PHASE-TRANSITION
  • RANDOM NETWORKS
  • STEADY-STATES
  • TRANSLATIONAL INVARIANCE
  • HYDRODYNAMICAL EQUATION
  • SPONTANEOUS BREAKING

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