Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains

2016/07/14 by Christian B. Mendl, Herbert Spohn · 13 citations
Materials Science · Mathematics · Physics and Astronomy · #Anharmonicity #Current (fluid) #Lattice (music) #Non-equilibrium thermodynamics #Nonlinear Photonic Systems #Organic and Molecular Conductors Research #Quantum many-body systems #Riemann problem #Statistical mechanics #Stochastic process #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1007/s10955-016-1626-5

published in Journal of Statistical Physics 166(3-4), 841-875 (Springer Science+Business Media) · 39 pages, 17 figures

arxiv created 2016/07/14 · openalex created_date 2016/09/16 · openalex publication_date 2016/10/04 · arxiv updated 2016/10/07 · openalex updated_date 2026/08/05

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.

Citations

• Hyperbolic systems of conservation laws II

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