Research output: Contribution to journal › Article

Original language | English |
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Article number | 073302 |

Journal | JOURNAL OF MATHEMATICAL PHYSICS |

Volume | 60 |

Issue number | 7 |

DOIs | |

Publication status | Published - 11 Jul 2019 |

TodaGHD7_jmp.pdf, 326 KB, application/pdf

27/06/2019

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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