(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model

TL;DR

This paper investigates the classical Neumann integrable model using a soft spherical constraint approach, demonstrating that the Generalized Gibbs Ensemble accurately predicts long-time behavior across various dynamic phases.

Contribution

It introduces a soft constraint version of the Neumann model and confirms the GGE's validity in describing its long-term dynamics across different phases.

Findings

GGE captures long-time averages of the soft model

Identifies a full dynamic phase diagram with multiple phases

Establishes conditions where strict and soft constraints are equivalent

Abstract

We study a classical integrable (Neumann) model describing the motion of a particle on the sphere, subject to harmonic forces. We tackle the problem in the infinite dimensional limit by introducing a soft version in which the spherical constraint is imposed only on average over initial conditions. We show that the Generalized Gibbs Ensemble captures the long-time averages of the soft model. We reveal the full dynamic phase diagram with extended, quasi-condensed, coordinate-, and coordinate and momentum-condensed phases. The scaling properties of the fluctuations allow us to establish in which cases the strict and soft spherical constraints are equivalent, confirming the validity of the GGE hypothesis for the Neumann model on a large portion of the dynamic phase diagram.