• 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}
}
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… 
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TLDR
This paper proves the convergence of their empirical spectral distributions to their mean densities of states, and explicitly compute the mean density of states of the Lax matrix of the Toda lattice with periodic boundary conditions with respect to the Gibbs ensemble.
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