Interrelations between dualities in classical integrable systems and classical-classical version of quantum-classical duality

TL;DR

This paper explores the spectral duality in classical integrable systems, connecting spin chains and Gaudin models through Lax matrices, and presents a classical-classical analogue of quantum-classical duality.

Contribution

It introduces a novel spectral duality transformation linking classical many-body systems and Gaudin models, and interprets Lax matrices as a classical version of quantum-classical duality.

Findings

Spectral duality relates spin chains and Gaudin models.

Lax matrices are represented in multi-pole form.

Classical-classical version of quantum-classical duality is proposed.

Abstract

We describe the Ruijsenaars' action-angle duality in classical many-body integrable systems through the spectral duality transformation relating the classical spin chains and Gaudin models. For this purpose, the Lax matrices of many-body systems are represented in the multi-pole (Gaudin-like) form by introducing a fictitious spectral parameter. This form of Lax matrices is also interpreted as classical-classical version of quantum-classical duality.