Equilibration Properties of Classical Integrable Field Theories

TL;DR

This paper investigates how classical integrable field theories reach equilibrium from far-from-equilibrium initial states, connecting classical and quantum descriptions through high occupation number limits and generalized statistical ensembles.

Contribution

It introduces a method to compute time averages in classical integrable field theories using a generalized LeClair-Mussardo formula linked to the GGE, addressing infinite gap solutions.

Findings

Time averages can be expressed via a generalized LeClair-Mussardo formula.

Provides a solution to the infinite gap problem in the inverse scattering method.

Establishes a connection between classical and quantum field theories at high occupation numbers.

Abstract

We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper $\hbar \rightarrow 0$ limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the Generalized Gibbs Ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the {\em infinite gap solutions} of the Inverse Scattering Method.