Journal of Statistical Physics

, Volume 160, Issue 4, pp 861–884 | Cite as

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

  • Herbert Spohn
  • Gabriel Stoltz


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 \(\alpha = 5/3\). As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.


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



We thank Christian Mendl for numerous instructive discussions, as well as Günther Schütz for stimulating comments on a preliminary version of this manuscript. H.S. is grateful for the support through the Institute for Advanced Study, Princeton, where the first steps in this project were accomplished and thanks David Huse for insisting on a complete classification.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Zentrum Mathematik and Physik DepartmentTU MünchenGarchingGermany
  2. 2.Université Paris-Est, CERMICS (ENPC), INRIAMarne-la-ValléeFrance

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