Microscopic shape of shocks in a domain growth model

Márton Balázs*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

15 Citations (Scopus)

Abstract

Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g., the inviscid Burgers equation for the simple exclusion process. The physical solutions of these partial differential equations develop discontinuities, called shocks. The microscopic structure of these shocks is of much interest and far from being well understood. We introduce a domain growth model in which we find a stationary (in time) product measure for the model, as seen from a defect tracer or second class particle, traveling with the shock. We also show that under some natural assumptions valid for a wider class of domain growth models, no other model has stationary product measure as seen from the moving defect tracer.

Original languageEnglish
Pages (from-to)511-524
Number of pages14
JournalJournal of Statistical Physics
Volume105
Issue number3-4
DOIs
Publication statusPublished - Nov 2001

Keywords

  • Second class particle
  • Shock solution

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