Nonlinear Fluctuating Hydrodynamics in One Dimension: The Case of Two Conserved Fields

Herbert Spohn, Gabriel Stoltz

Research output: Contribution to journalArticlepeer-review

52 Scopus citations

Abstract

We study the BS model, which is a one-dimensional lattice field theory taking real values. Its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges. The BS model has two locally conserved fields. The peak structure of their steady state space–time correlations is determined through numerical simulations and compared with nonlinear fluctuating hydrodynamics, which predicts a traveling peak with KPZ scaling function and a standing peak with a scaling function given by the maximally asymmetric Lévy distribution with parameter α=5/3. As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.

Original languageEnglish
Pages (from-to)861-884
Number of pages24
JournalJournal of Statistical Physics
Volume160
Issue number4
DOIs
StatePublished - 29 Aug 2015

Keywords

  • KPZ equation
  • Mode-coupling theory
  • Thermal transport in one dimensional systems

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