Phase separation and coarsening in one-dimensional driven diffusive systems: Local dynamics leading to long-range Hamiltonians

MR Evans*, Y Kafri, HM Koduvely, D Mukamel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A driven system of three species of particles diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational symmetry is given. We show that for the special case where the three densities are equal the model obeys detailed balance, and the steady-state distribution is governed by a Hamiltonian with asymmetric long-range interactions. This provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension. The steady state of finite-size systems is studied using a generalized matrix product ansatz. The coarsening process leading to phase separation is studied numerically and in a mean-field model. The system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size. The typical domain size is shown to grow logarithmically in time. Generalizations to a larger number of species are discussed.

Original languageEnglish
Pages (from-to)2764-2778
Number of pages15
JournalPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
Volume58
Issue number3
Publication statusPublished - Sep 1998

Keywords

  • SPONTANEOUS SYMMETRY-BREAKING
  • ASYMMETRIC EXCLUSION MODEL
  • DOMAIN GROWTH

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