Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 046, 23 pages      math-ph/0703045      https://doi.org/10.3842/SIGMA.2007.046
Contribution to the Vadim Kuznetsov Memorial Issue

Qualitative Analysis of the Classical and Quantum Manakov Top

Evguenii Sinitsyn a and Boris Zhilinskii b
a) Physics Department, Tomsk State University, 634050 Tomsk, Russia
b) Université du Littoral, UMR du CNRS 8101, 59140 Dunkerque, France

Received 20 October, 2006, in final form 19 January, 2007; Published online March 13, 2007

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.

Key words: Manakov top; energy-momentum diagram; monodromy.

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