Quantum-classical duality for Gaudin magnets with boundary

TL;DR

This paper reveals a deep connection between quantum Gaudin models with boundary conditions and classical Calogero-Moser systems, extending previous dualities to new boundary cases and root systems.

Contribution

It establishes a quantum-classical duality for Gaudin models with boundary conditions linked to classical Lie algebra root systems, generalizing earlier results.

Findings

Spectral identification between Gaudin Hamiltonians and classical particle velocities

All integrals of motion of the classical system vanish under this duality

Extension of quantum-classical duality to boundary conditions and root systems B, C, D

Abstract

We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians $H_j^{\rm G}$ with particles velocities $\dot q_j$ of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic boundary conditions and Calogero-Moser models associated with the root system of the type A.