Journal of Statistical Physics

, Volume 166, Issue 3–4, pp 841–875 | Cite as

Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains

Article

Abstract

The nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain-wall state, in which the two half lattices are prepared in equilibrium with distinct parameters. We analyse the Riemann problem for the corresponding Euler equations and, in specific cases, compare with molecular dynamics. Additionally, the fluctuations of time-integrated currents are investigated. In analogy with the KPZ equation, their typical fluctuations should be of size \(t^{1/3}\) and have a Tracy–Widom GUE distributed amplitude. The proper extension to anharmonic chains is explained and tested through molecular dynamics. Our results are calibrated against the stochastic LeRoux lattice gas.

Keywords

Fluid dynamics Hydrodynamic waves Statistical mechanics of classical fluids Nonequilibrium thermodynamics 

Notes

Acknowledgments

The work of HS has been supported as a Simons Distinguished Visiting Scholar, when visiting the KITP early 2016. CM acknowledges support from the Alexander von Humboldt Foundation and computing resources of the Leibniz-Rechenzentrum.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Geballe Laboratory for Advanced MaterialsStanford UniversityStanfordUSA
  2. 2.Stanford Institute for Materials and Energy SciencesSLAC National Accelerator LaboratoryMenlo ParkUSA
  3. 3.Zentrum Mathematik and Physik DepartmentTechnische Universität MünchenGarching bei MünchenGermany

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