Eur. Phys. J. E (2021) 44: 29
https://doi.org/10.1140/epje/s10189-021-00046-5

Regular Article - Flowing Matter

Condensation transition and ensemble inequivalence in the discrete nonlinear Schrödinger equation

¹ Gran Sasso Science Institute, Viale F. Crispi 7, 67100, L’Aquila, Italy
² Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019, Sesto Fiorentino, Italy
³ Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Italy
⁴ Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Italy
⁵ LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405, Orsay, France

^a giacomo.gradenigo@gssi.it

Received: 16 December 2020
Accepted: 25 February 2021
Published online: 12 March 2021

Abstract

The thermodynamics of the discrete nonlinear Schrödinger 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.