Exact Thermodynamics and Transport in the Classical Sine-Gordon Model

Abstract

We revisit the exact thermodynamic description of the classical sine-Gordon field theory, a notorious integrable model. We found that existing results in the literature based on the soliton-gas picture did not correctly take into account light, but extended, solitons and thus led to incorrect results. This issue is regularized upon requantization: we derive the correct thermodynamics by taking the semiclassical limit of the quantum model. Our results are then extended to transport settings by means of Generalized Hydrodynamics.

33 pages, 4 figures

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Cited by in corpus (18)

• Generalized hydrodynamics: a perspective
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• The sine-Gordon model from coupled condensates: a Generalized Hydrodynamics viewpoint
• Exact large-scale fluctuations of the phase field in the sine-Gordon model
• New classical integrable systems from generalized $T\bar{T}$-deformations
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model
• Landau-Lifschitz magnets: exact thermodynamics and transport
• Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics
• Dynamical separation of charge and energy transport in one-dimensional Mott insulators
• Quantum simulating continuum field theories with large-spin lattice models
• Non-equilibrium time evolution in the sine-Gordon model revisited
• Exact mapping from the $(3+1)$-dimensional Skyrme model to the $(1+1)$-dimensional sine-Gordon theory and some applications
• Sine-Gordon dynamics in spin transport
• Anomalous charge transport in the sine-Gordon model
• Sine-Gordon model at finite temperature: the method of random surfaces
• Observation of a generalized Gibbs ensemble in photonics
• Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions
• Observation of sine-Gordon-like solitons in a spinor Bose-Einstein condensate