Quantum Gaudin model and classical KP hierarchy

Abstract

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.

12 pages, written for proceedings of the International conference "Physics and Mathematics of Nonlinear Phenomena", Gallipoli, 22-29 June 2013

References in corpus (4)

• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• On Three Dimensional Quiver Gauge Theories and Integrability
• From Characters to Quantum (Super)Spin Chains via Fusion
• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz

Cited by in corpus (1)

• Supersymmetric quantum spin chains and classical integrable systems