Qualitative Analysis of the Classical and Quantum Manakov Top
Evguenii Sinitsyn, Boris Zhilinskii
TL;DR
This paper explores the classical and quantum Manakov top, analyzing their energy-momentum diagrams and joint spectra, and introduces quantum monodromy to understand spectral evolution across singularities.
Contribution
It provides a detailed qualitative analysis of the classical and quantum Manakov top, including the first introduction of quantum monodromy in this context.
Findings
Energy-momentum diagram characterized for classical case
Joint quantum spectrum analyzed for quantum case
Quantum monodromy transformation defined across singular strata
Abstract
Qualitative features of the Manakov top are discussed for the classical and quantum versions of the problem. Energy-momentum diagram for this integrable classical problem and quantum joint spectrum of two commuting observables for associated quantum problem are analyzed. It is demonstrated that the evolution of the specially chosen quantum cell through the joint quantum spectrum can be defined for paths which cross singular strata. The corresponding quantum monodromy transformation is introduced.
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