可积系统
数学
周期边界条件
哈密顿量(控制论)
松驰对
格子(音乐)
数学分析
非线性系统
吉布斯测度
边值问题
数学物理
物理
量子力学
声学
数学优化
作者
Guido Mazzuca,Guido Mazzuca
标识
DOI:10.1007/s00220-023-04642-8
摘要
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 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 $$\beta $$ β -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.
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