Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schr\"odinger Equation

TL;DR

This paper analyzes the thermodynamics of the discrete nonlinear Schrödinger equation near infinite temperature, revealing a phase transition and ensemble inequivalence, with implications for cold atom experiments.

Contribution

It provides an explicit microcanonical analysis of the phase transition and ensemble inequivalence in the discrete nonlinear Schrödinger equation using large-deviation techniques.

Findings

First-order phase transition at infinite temperature line

Ensemble inequivalence in the condensed phase

Potential for experimental observation in cold atom lattices

Abstract

The thermodynamics of the discrete nonlinear Schr\"odinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a thermalized phase and a condensed (localized) one occurs at the infinite-temperature line. Inequivalence between statistical ensembles characterizes the condensed phase, where the grand-canonical representation does not apply. The control over finite size corrections of the microcanonical partition function allows to design an experimental test of delocalized negative-temperature states in lattices of cold atoms.