Burgers equation from non-thermal stationary states in nearly-integrable gases

TL;DR

This paper demonstrates that in nearly-integrable gases with non-thermal states, the large-scale density dynamics can be described by Burgers equation, revealing novel hydrodynamic behavior beyond standard diffusion.

Contribution

It shows that non-thermal states in nearly-integrable gases lead to Burgers equation dynamics, with explicit calculations of transport coefficients using Chapman-Enskog theory.

Findings

Burgers equation describes density dynamics in non-thermal states.

Explicit diffusion and nonlinear coefficients match numerical simulations.

Hydrodynamics depends on parity-breaking non-thermal states.

Abstract

When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets altered, when transport is investigated on top of long-lived non-thermal states. Remarkably, for states non-invariant under parity we find Burgers equation arising in the hydrodynamic limit. We explicitly compute the diffusion constant and nonlinear advective coefficient of the Burgers equation using a variant of the Chapman-Enskog theory. We find an excellent agreement between our theory and numerical simulations of a simplified model of stochastic two-body collisions. Our conclusions are based only on Galilean invariance, existence of a small system-bath coupling parameter and a small momentum exchange between the system and the bath particles during two-body scattering.