Analytic representations of quantum systems with Theta functions

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.

Grantor dc:publisher.institution

University of Bradford

Year dc:date.issued

2015

Author dc:creator

• Evangelides, Pavlos

Advisors dc:contributor.advisor

• Vourdas, Apostolos
• Lei, Ci

• Analytic functions; Theta functions; Bargmann functions; Finite quantum systems

Statement dc:rights

• <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>.

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10454/14366

OAI identifier oai:identifier

oai:bradscholars.brad.ac.uk:10454/14366