Qualitative analysis of the classical and quantum Manakov top

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.

Original language	English
Article number	046
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	3
DOIs	https://doi.org/10.3842/SIGMA.2007.046
Publication status	Published - 2007
Externally published	Yes

Keywords

Energy-momentum diagram
Manakov top
Monodromy

ASJC Scopus subject areas

Analysis
Geometry and Topology
Mathematical Physics

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10.3842/SIGMA.2007.046

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title = "Qualitative analysis of the classical and quantum Manakov top",

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.",

keywords = "Energy-momentum diagram, Manakov top, Monodromy",

author = "Evguenii Sinitsyn and Boris Zhilinskii",

year = "2007",

doi = "10.3842/SIGMA.2007.046",

language = "English",

volume = "3",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

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AU - Zhilinskii, Boris

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AB - 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.

KW - Energy-momentum diagram

KW - Manakov top

KW - Monodromy

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