2024/05/26 by А. В. Михайлов, Mikhailov, A., T. Skrypnyk +1 · 3 citations
Mathematics · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2405.16532
openalex publication_date 2024/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this letter, we revisit the quantisation problem for a fundamental model of classical mechanics - the Zhukovsky-Volterra top. We have discovered a four-parametric pencil of compatible Poisson brackets, comprising two quadratic and two linear Poisson brackets. Using the quantisation ideal method, we have identified two distinct quantisations of the Zhukovsky-Volterra top. The first type corresponds to the universal enveloping algebras of so(3), leading to Lie-Poisson brackets in the classical limit. The second type can be regarded as a quantisation of the four-parametric inhomogeneous quadratic Poisson pencil. We discuss the relationships between the quantisations obtained in our paper, Sklyanin's quantisation of the Euler top, and Levin-Olshanetsky-Zotov's quantisation of the Zhukovsky-Volterra top.