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Regular version of the site

Article

Quantum-classical duality for Gaudin magnets with boundary

Nuclear Physics B. 2020. Vol. 952. No. March 2020. P. 1-20.
Zabrodin A., Zotov A., Vasilyev M.

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^G_j 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.