Three-stage thermalisation of a quasi-integrable system

Leonardo Biagetti; Guillaume Cecile; Jacopo De Nardis

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arXiv · 2307.05379

Three-stage thermalisation of a quasi-integrable system

Leonardo Biagetti·Guillaume Cecile·Jacopo De Nardis

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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.

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Leonardo Biagetti, Guillaume Cecile, Jacopo De Nardis. 2023-07-11. Three-stage thermalisation of a quasi-integrable system. https://arxiv.org/abs/2307.05379

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