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Dynamics of hard rods with initial domain wall state

Research output: Contribution to journalArticle

Benjamin Doyon, Herbert Spohn

Original languageEnglish
Article number073210
Number of pages21
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2017
DOIs
Publication statusPublished - 27 Jul 2017

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  • Dynamics of hard rods_DOYON_Firstpublished27July2017_GREEN AAM

    hydrohardrodsAv10.pdf, 332 KB, application/pdf

    27/07/2018

    Accepted author manuscript

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    This is an author-created, un-copyedited version of an article accepted for publication in Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.

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Abstract

Inspired by recent results on the non-equilibrium dynamics of many-body quantum systems, we study the classical hard rod problem in one dimension with initial domain wall condition. Hard rods are an integrable system, in the sense that for each velocity the density of particles is locally conserved. It was proven by Boldrighini et al (1983 J. Stat. Phys. 31 577) that on the hydrodynamic space-time scale, the fluid of hard rods satisfies Euler-type equations which comprise all conservation laws. We provide the general solution to these equations on the line, with an initial condition where the left and right halves are, asymptotically, in different states. The solution is interpreted as being composed of a continuum of contact discontinuities, one for each velocity. This is a classical counterpart of the transport problem solved recently in quantum integrable systems. We also discuss the Navier–Stokes (viscous) corrections, and study its effect on the broadening of the contact discontinuity and on entropy production.

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