Condensation transition and ensemble inequivalence in the discrete nonlinear Schrodinger equation

The thermodynamics of the discrete nonlinear Schrodinger 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.

Automated summary

The study explicitly solves the thermodynamics of the discrete nonlinear Schrodinger equation near infinite temperature in the microcanonical ensemble through large deviation techniques, revealing a first-order phase transition between a thermalized phase and a condensed phase along the infinite-temperature line. In the condensed phase, inequivalence between statistical ensembles is observed, highlighting the inability of the grand-canonical representation. Control over finite-size corrections of the microcanonical partition function allows for the design of an experimental test of delocalized negative-temperature states in lattices of cold atoms.