Quantum Gaudin model and classical KP hierarchy

Physics and Mathematics of Nonlinear Phenomena 2013

Zabrodin, A.^1,2,3

Institute of Biochemical Physics, 4 Kosygina, 119334, Moscow, Russia^1

ITEP, 25 B. Cheremushkinskaya, 117218, Moscow, Russia^2

National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow 101000, Russia^3

关键词: Eigenvalues;    Generating functions;    Hirota equation;    Integrals of motion;    Spectral parameters;    T-operators;    Twisted boundary conditions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012047/pdf
DOI  :  10.1088/1742-6596/482/1/012047

来源: IOP

【 摘 要 】

This short note is a review of the intriguing connection between the quantum Gaudin model and the classical KP hierarchy recently established in [1]. We construct the generating function of integrals of motion for the quantum Gaudin model with twisted boundary conditions (the master T-operator) and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. This implies that zeros of eigenvalues of the master T-operator in the spectral parameter have the same dynamics as the Calogero-Moser system of particles.