Condensation in the Zero Range Process: Stationary and Dynamical Properties

Stefan Großkinsky, Gunter M. Schütz, Herbert Spohn

Research output: Contribution to journalArticlepeer-review

163 Scopus citations

Abstract

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.

Original languageEnglish
Pages (from-to)389-410
Number of pages22
JournalJournal of Statistical Physics
Volume113
Issue number3-4
DOIs
StatePublished - Nov 2003

Keywords

  • Equivalence of ensembles
  • Nonequilibrium phase transition
  • Relative entropy
  • Zero range process

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