Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model

Alvise Bastianello; Benjamin Doyon; Gérard Watts; Takato Yoshimura

doi:10.21468/SciPostPhys.4.6.045

Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model

Alvise Bastianello, Benjamin Doyon, Gérard Watts, Takato Yoshimura

SISSA Trieste

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Abstract

Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz of quantum models, which we extend to generalized Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic and radiative modes of classical fields. We observe that the quasi-particle formulation of GHD remains valid for radiative modes, even though these do not display particle-like properties in their precise dynamics. We point out that because of a UV catastrophe similar to that of black body radiation, radiative modes suffer from divergences that restrict the set of finite-average observables; this set is larger for GGEs with higher conserved charges. We concentrate on the sinh-Gordon model, which only has radiative modes, and study transport in the domain-wall initial problem as well as Euler-scale correlations in GGEs. We confirm a variety of exact GHD predictions, including those coming from hydrodynamic projection theory, by comparing with Metropolis numerical evaluations.

Original language	English
Journal	SciPost
DOIs	https://doi.org/10.21468/SciPostPhys.4.6.045
Publication status	Published - 30 Jun 2018

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10.21468/SciPostPhys.4.6.045Licence: CC BY

Generalized hydrodynamics of classical_BASTIANELLO_Accepted19June2018_GOLD VoR (CC BY)Final published version, 819 KBLicence: CC BY

https://arxiv.org/pdf/1712.05687

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title = "Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model",

abstract = "Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz of quantum models, which we extend to generalized Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic and radiative modes of classical fields. We observe that the quasi-particle formulation of GHD remains valid for radiative modes, even though these do not display particle-like properties in their precise dynamics. We point out that because of a UV catastrophe similar to that of black body radiation, radiative modes suffer from divergences that restrict the set of finite-average observables; this set is larger for GGEs with higher conserved charges. We concentrate on the sinh-Gordon model, which only has radiative modes, and study transport in the domain-wall initial problem as well as Euler-scale correlations in GGEs. We confirm a variety of exact GHD predictions, including those coming from hydrodynamic projection theory, by comparing with Metropolis numerical evaluations.",

author = "Alvise Bastianello and Benjamin Doyon and G{\'e}rard Watts and Takato Yoshimura",

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TY - JOUR

T1 - Generalized hydrodynamics of classical integrable field theory

T2 - the sinh-Gordon model

AU - Bastianello, Alvise

AU - Doyon, Benjamin

AU - Watts, Gérard

AU - Yoshimura, Takato

PY - 2018/6/30

Y1 - 2018/6/30

N2 - Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz of quantum models, which we extend to generalized Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic and radiative modes of classical fields. We observe that the quasi-particle formulation of GHD remains valid for radiative modes, even though these do not display particle-like properties in their precise dynamics. We point out that because of a UV catastrophe similar to that of black body radiation, radiative modes suffer from divergences that restrict the set of finite-average observables; this set is larger for GGEs with higher conserved charges. We concentrate on the sinh-Gordon model, which only has radiative modes, and study transport in the domain-wall initial problem as well as Euler-scale correlations in GGEs. We confirm a variety of exact GHD predictions, including those coming from hydrodynamic projection theory, by comparing with Metropolis numerical evaluations.

AB - Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz of quantum models, which we extend to generalized Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic and radiative modes of classical fields. We observe that the quasi-particle formulation of GHD remains valid for radiative modes, even though these do not display particle-like properties in their precise dynamics. We point out that because of a UV catastrophe similar to that of black body radiation, radiative modes suffer from divergences that restrict the set of finite-average observables; this set is larger for GGEs with higher conserved charges. We concentrate on the sinh-Gordon model, which only has radiative modes, and study transport in the domain-wall initial problem as well as Euler-scale correlations in GGEs. We confirm a variety of exact GHD predictions, including those coming from hydrodynamic projection theory, by comparing with Metropolis numerical evaluations.

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DO - 10.21468/SciPostPhys.4.6.045

M3 - Article

SN - 2542-4653

JO - SciPost

JF - SciPost

ER -

Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model

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