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Generalized hydrodynamics of the classical Toda system

Research output: Contribution to journalArticle

Original languageEnglish
Article number073302
JournalJOURNAL OF MATHEMATICAL PHYSICS
Volume60
Issue number7
DOIs
Publication statusPublished - 11 Jul 2019

Documents

  • TodaGHD7-jmp

    TodaGHD7_jmp.pdf, 326 KB, application/pdf

    27/06/2019

King's Authors

Abstract

We obtain the exact generalized hydrodynamics for the integrable Toda system. The Toda system can be seen in a dual way, both as a gas and as a chain. In the gas point of view, using the elastic and factorized scattering of Toda particles, we obtain the generalized free energy and exact average currents and write down the Euler hydrodynamic equations. This is written both as a continuity equation for the density of asymptotic momenta and in terms of normal modes. This is based on the classical thermodynamic Bethe ansatz (TBA), with a single quasiparticle type of Boltzmann statistics. By explicitly connecting chain and gas conserved densities and currents, we then derive the thermodynamics and hydrodynamics of the chain. As the gas and chain have different notions of length, they have different hydrodynamics, and, in particular, the velocities of normal modes differ. We also give a derivation of the classical TBA equations for the gas thermodynamics from the factorized scattering of Toda particles.

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