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arXiv · 2212.00276

Phase Transition for Discrete Non Linear Schr\"odinger Equation in Three and Higher Dimensions

Partha S. Dey·Kay Kirkpatrick·Kesav Krishnan
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Abstract

We analyze the thermodynamics of the focusing discrete nonlinear Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$ and under a model with two parameters, representing inverse temperature and strength of the nonlinearity, respectively. We prove the existence of limiting free energy and analyze the phase diagram for general $d,p$. We also prove the existence of a continuous phase transition curve that divides the parametric plane into two regions involving the appearance or non-appearance of solitons. Appropriate upper and lower bounds for the curve are constructed. We also look at the typical behavior of a function chosen from the Gibbs measure for certain parts of the phase diagram.

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Partha S. Dey, Kay Kirkpatrick, Kesav Krishnan. 2022-12-01. Phase Transition for Discrete Non Linear Schr\"odinger Equation in Three and Higher Dimensions. https://arxiv.org/abs/2212.00276

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