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

TL;DR

This paper extends generalized hydrodynamics to classical integrable field theories, specifically the sinh-Gordon model, accounting for both solitonic and radiative modes, and confirms theoretical predictions with numerical simulations.

Contribution

It develops a GHD framework for classical integrable fields including radiative modes and demonstrates its validity through the sinh-Gordon model.

Findings

GHD applies to radiative modes despite their particle-like dynamics

Radiative modes exhibit UV divergences limiting observable sets

Numerical results confirm GHD predictions for transport and correlations

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.