Quantum-classical correspondence

Mikhail Vasilev (University of Glasgow)

Tuesday 17th February 16:00-17:00
Maths 311B

Abstract

Quantum–classical correspondence is a relation between the spectra of quantum integrable systems, such as XXX/XXZ spin chains and the corresponding Gaudin models, and classical many-body integrable systems like the Ruijsenaars–Schneider and Calogero–Moser systems. The first hint of such a relationship appeared in the work of A. Givental and B. Kim on the quantum cohomology of flag varieties in 1993. In 2013, A. Gorsky, A. Zabrodin, and A. Zotov established a direct relation between XXX-type integrable models and the corresponding Ruijsenaars–Calogero integrable systems using the technique of the nested Bethe ansatz. Later, this relation was generalised to trigonometric integrable models, supersymmetric spin chains, root systems other than type A, and certain limiting cases were also studied. I will try to give an overview of this subject, focusing on particular examples.

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