Shocks, rarefaction waves, and current fluctuations for anharmonic chains

TL;DR

This paper investigates the nonequilibrium dynamics of anharmonic chains, analyzing shock and rarefaction wave formation, current fluctuations, and comparing theoretical predictions with molecular dynamics simulations.

Contribution

It extends the understanding of current fluctuations and wave dynamics in anharmonic chains, connecting them with KPZ universality and Tracy-Widom distributions.

Findings

Shock and rarefaction wave solutions are characterized.

Current fluctuations follow Tracy-Widom GUE distribution.

Results are validated against stochastic LeRoux lattice gas.

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.