Mean-field theory of the DNLS equation at positive and negative absolute temperatures

2025/11/12 by Giusfredi, Michele, Iubini, Stefano, Politi, Antonio +1 · 1 citation
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2511.09206

Abstract

The Discrete Non Linear Schrödinger (DNLS) model, due to the existence of two conserved quantities, displays an equilibrium transition between a homogeneous phase at positive absolute temperature and a localized phase at negative absolute temperature. Here, we provide a mean-field theory of DNLS and show that this approximation is semi-quantitatively correct in the whole phase diagram, becoming exact in proximity of the transition. Our mean-field theory shows that the passage from stable positive-temperature to metastable negative-temperature states is smooth.

Citations

• Dynamics of localized states in the stochastic discrete nonlinear Schrödinger equation
• Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
• Infinite-temperature thermostats by energy localization in a nonequilibrium setup

Cited by

• The stochastic discrete nonlinear Schrödinger equation: microscopic derivation and finite-temperature phase transition

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