Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation

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.

arXiv comment6 pages, 3 figures

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Cited by in corpus (23)

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• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Chaos and localization in the Discrete Nonlinear Schrödinger Equation
• Large deviations in chaotic systems: exact results and dynamical phase transition
• Finite-size localization scenarios in condensation transitions
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• On the foundations of statistical mechanics
• Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
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• Condensation induced by coupled transport processes
• Intensity pseudo-localized phase in the glassy random laser
• Data-driven analysis of annual rain distributions
• Localization in boundary-driven lattice models
• Onsager coefficients in a coupled-transport model displaying a condensation transition
• Subleading-order theory for condensation transitions in large deviations of sums of independent and identically distributed random variables
• Symplectic Quantization: numerical results for the Feynman propagator on a 1+1 lattice and the theoretical relation with Quantum Field Theory
• Relaxation dynamics and finite-size effects in a simple model of condensation
• Infinite-temperature thermostats by energy localization in a nonequilibrium setup
• Extreme value statistics in a continuous time branching process: a pedagogical primer
• Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
• Frozen dynamics of a breather induced by an adiabatic invariant