The action-angle Wigner function: A discrete, finite and algebraic phase space formalism

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dc.citation.epage6383en_US
dc.citation.issueNumber36en_US
dc.citation.spage6357en_US
dc.citation.volumeNumber33en_US
dc.contributor.authorHakioǧlu, T.en_US
dc.contributor.authorTepedelenlioǧlu, E.en_US
dc.date.accessioned2016-02-08T10:37:27Z
dc.date.available2016-02-08T10:37:27Z
dc.date.issued2000en_US
dc.departmentDepartment of Physicsen_US
dc.description.abstractThe action-angle representation in quantum mechanics is conceptually quite different from its classical counterpart and motivates a canonical discretization of the phase space. In this work, a discrete and finite-dimensional phase space formalism, in which the phase space variables are discrete and the time is continuous, is developed and the fundamental properties of the discrete Weyl-Wigner-Moyal quantization are derived. The action-angle Wigner function is shown to exist in the semi-discrete limit of this quantization scheme. A comparison with other formalisms which are not explicitly based on canonical discretization is made. Fundamental properties that an action-angle phase space distribution respects are derived. The dynamical properties of the action-angle Wigner function are analysed for discrete and finite-dimensional model Hamiltonians. The limit of the discrete and finite-dimensional formalism including a discrete analogue of the Gaussian wavefunction spread, viz. the binomial wavepacket, is examined and shown by examples that standard (continuum) quantum mechanical results can be obtained as the dimension of the discrete phase space is extended to infinity.en_US
dc.identifier.doi10.1088/0305-4470/33/36/307en_US
dc.identifier.issn0305-4470
dc.identifier.urihttp://hdl.handle.net/11693/24998
dc.language.isoEnglishen_US
dc.relation.isversionofhttp://dx.doi.org/10.1088/0305-4470/33/36/307en_US
dc.source.titleJournal of Physics A: Mathematical and Generalen_US
dc.titleThe action-angle Wigner function: A discrete, finite and algebraic phase space formalismen_US
dc.typeArticleen_US

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