Shocks, rarefaction waves, and current fluctuations for anharmonic chains

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.

39 pages, 17 figures

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• Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics
• The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
• Entropy growth during free expansion of an ideal gas
• Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
• A splash in a one-dimensional cold gas
• High-low pressure domain wall for the classical Toda lattice
• Correlation Functions for a Chain of Short Range Oscillators