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Title: Analytic representations of quantum systems with Theta functions
Author: Evangelides, Pavlos
ISNI:       0000 0004 6495 4620
Awarding Body: University of Bradford
Current Institution: University of Bradford
Date of Award: 2015
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Analytic functions ; Theta functions ; Bargmann functions ; Finite quantum systems