Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
Statistical Mechanics
2022-04-06 v3 Mathematical Physics
math.MP
Abstract
Ablowitz and Ladik discovered a discretization which preserves the integrability of the nonlinear Schroedinger equation in one dimension. We compute the generalized free energy of this model and determine the GGE averaged fields and currents. They are linked to the mean-field circular unitary matrix ensemble (CUE). The resulting hydrodynamic equations follow the pattern already known from other integrable many-body systems. Studied is also the discretized modified Korteweg-de-Vries equation which turns out to be related to the beta Jacobi log gas.
Keywords
Cite
@article{arxiv.2107.04866,
title = {Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation},
author = {Herbert Spohn},
journal= {arXiv preprint arXiv:2107.04866},
year = {2022}
}
Comments
27 pages, improved and expanded version