Three-stage thermalisation of a quasi-integrable system

TL;DR

This paper investigates the thermalisation process of a classical one-dimensional hard rod system under external periodic fields, revealing a universal three-stage process involving Euler hydrodynamics, turbulence, and viscous hydrodynamics.

Contribution

It introduces a detailed three-stage thermalisation framework for a classical integrable system under external perturbations, highlighting universal features applicable to other many-body integrable systems.

Findings

Early dynamics described by Euler hydrodynamics

Observation of a weak turbulent phase during evolution

Final thermalisation governed by viscous hydrodynamics

Abstract

We consider a system of classical hard rods or billiard balls in one dimension, initially prepared in a Bragg-pulse state at a given temperature and subjected to external periodic fields. We show that at late times the system always thermalises in the thermodynamic limit via a 3-stages process characterised by: an early phase where the dynamics is well described by Euler hydrodynamics, a subsequent where a (weak) turbulent phase is observed and where hydrodynamic gradient expansion can be broken, and a final one where the gas thermalises according to a viscous hydrodynamics. As the hard rod gas shares the same large-scale hydrodynamics as other quantum and classical integrable systems, we expect these features to universally characterise all many-body integrable systems in generic external potentials.