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Analytic representations of quantum systems with Theta functions

Evangelides, Pavlos
Publication Date
2015
End of Embargo
Supervisor
Vourdas, Apostolos
Lei, Ci
Keywords
Analytic functions; Theta functions; Bargmann functions; Finite quantum systems
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Creative Commons License
The University of Bradford theses are licenced under a Creative Commons Licence.
Peer-Reviewed
Open Access status
Accepted for publication
Institution
University of Bradford
Department
Faculty of Engineering and Informatics Department of Computing
Awarded
2015
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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.
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http://hdl.handle.net/10454/14366
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Type
Thesis
Qualification name
PhD
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