• Corpus ID: 235742966

# Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, Circular $\beta$-ensemble and double confluent Heun equation

@inproceedings{Grava2021GeneralizedGE,
title={Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, Circular \$\beta\$-ensemble and double confluent Heun equation},
author={Tamara Grava and Guido Mazzuca},
year={2021}
}
• Published 5 July 2021
• Mathematics
Abstract We consider the discrete defocusing nonlinear Schrödinger equation in its integrable version, which is called defocusing Ablowitz-Ladik lattice. We consider periodic boundary conditions with period N and initial data sample according to the Generalized Gibbs ensemble. In this setting, the Lax matrix of the Ablowitz-Ladik lattice is a random CMV-periodic matrix and it is related to the Killip-Nenciu Circular β-ensemble at high-temperature. We obtain the generalized free energy of the…
3 Citations

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