# Equilibration Properties of Classical Integrable Field Theories

### Andrea De Luca 1 Giuseppe Mussardo 2, 3

#### Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2016, 064011

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.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
• 3. ICTP - International Center for Theoretical Physics [Trieste]