Generalized Gibbs Ensemble of the Ablowitz-Ladik Lattice, Circular β-Ensemble and Double Confluent Heun Equation

被引：0

作者：

Grava, Tamara ^{[1
,2
,3
]}

Mazzuca, Guido ^{[2
,4
]}

机构：

[1] Univ Bristol, Sch Math, Fry Bldg, Bristol BS8 1UG, England

[2] Sissa, Math Area, Via Bonomea 265, I-34136 Trieste, Italy

[3] INFN Sez Trieste, Trieste, Italy

[4] Royal Inst Technol, Math, Lindstedtsagen 25, S-11428 Stockholm, Sweden

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 399卷 / 03期

关键词：

ORTHOGONAL POLYNOMIALS; STATISTICAL-MECHANICS; HAMILTONIAN STRUCTURE; POISSON STATISTICS; MODEL; FLUCTUATIONS;

D O I：

10.1007/s00220-023-04642-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the discrete defocusing nonlinear Schrodinger equation in its integrable version, which is called defocusing Ablowitz-Ladik lattice. We consider periodic boundary conditions with period N and initial data sampled 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 beta-ensemble at high-temperature. We obtain the generalized free energy of the Ablowitz-Ladik lattice and the density of states of the random Lax matrix by establishing a mapping to the one-dimensional log-gas. For the Gibbs measure related to the Hamiltonian of the Ablowitz-Ladik flow, we obtain the density of states via a particular solution of the double-confluent Heun equation.

引用

页码：1689 / 1729

页数：41

共 13 条

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[4] Generalized Gibbs Ensemble of the Ablowitz–Ladik Lattice, Circular β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-Ensemble and Double Confluent Heun Equation
Tamara Grava
Guido Mazzuca
[J]. Communications in Mathematical Physics, 2023, 399 (3) : 1689 - 1729
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Vidmar, Lev
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