报告时间：2025年04月10日 15:30开始
报 告 人：Alexander V. Mikhailov (英国利兹大学教授）
报告地点：9-305
报告题目：Quantisation of the Euler top in a constant external field
报告摘要: We revisit the quantisation problem for a fundamental model of classical mechanics-the Euler top in a constant external field, also known as the Zhukovsky-Volterra model. Using the quantisation ideal method, we construct a quantisation that depends on five arbitrary parameters. This can be interpreted as a quantisation of the four-parameter inhomogeneous quadratic Poisson structure underlying the classical mechanical system.
In particular, the Euler top in a constant external field admits a Poisson pencil formed by two compatible linear Poisson brackets. One of these corresponds to the standard Poisson structure on so(3), whose quantisation has widespread applications in quantum chemistry, nuclear physics, and elementary particle theory. We propose a quantisation of the entire Poisson pencil and analyse the spectrum of the corresponding quantum Hamiltonian for a top with axial symmetry. Our results reveal that the spectrum depends on the pencil parameter, suggesting that the effects of the resulting bi-quantum structure may, in principle, be observable experimentally.
报告人简介：Alexander V.Mikhailov，英国利兹大学数学学院教授。从事可积系统的研究，特别是可积系统、非对易可积系统分类和量化问题。1978年在朗道理论物理研究所获得理论和数学物理博士学位，1987年全博士学位。剑桥大学克莱尔·霍尔学院终身院士。组织了多个会议和研讨会，并在国际期刊上发表了100多篇论文，引用次数超过7500次。
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