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    Analytic representations of quantum systems with Theta functions

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    Publication date
    2015
    Author
    Evangelides, Pavlos
    Supervisor
    Vourdas, Apostolos
    Lei, Ci
    Keyword
    Analytic functions; Theta functions; Bargmann functions; Finite quantum systems
    Rights
    Creative Commons License
    The University of Bradford theses are licenced under a Creative Commons Licence.
    Institution
    University of Bradford
    Department
    Faculty of Engineering and Informatics Department of Computing
    Awarded
    2015
    
    Metadata
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    Abstract
    Quantum systems in a d-dimensional Hilbert space are considered, where the phase spase is Z(d) x Z(d). An analytic representation in a cell S in the complex plane using Theta functions, is defined. The analytic functions have exactly d zeros in a cell S. The reproducing kernel plays a central role in this formalism. Wigner and Weyl functions are also studied. Quantum systems with positions in a circle S and momenta in Z are also studied. An analytic representation in a strip A in the complex plane is also defined. Coherent states on a circle are studied. The reproducing kernel is given. Wigner and Weyl functions are considered.
    URI
    http://hdl.handle.net/10454/14366
    Type
    Thesis
    Qualification name
    PhD
    Collections
    Theses

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