{"id":{"repo_id":"bradford","oai_identifier":"oai:bradscholars.brad.ac.uk:10454/14366"},"canonical_url":"https://search.dev.ndltd.org/etd/bradford/oai:bradscholars.brad.ac.uk:10454/14366","repository":{"repo_id":"bradford","name":"University of Bradford","base_url":"https://bradscholars.brad.ac.uk/oai/request"},"display":{"title":"Analytic representations of quantum systems with Theta functions","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Evangelides, Pavlos"],"institution":"University of Bradford","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Vourdas, Apostolos","Lei, Ci"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-24T01:14:32Z","subjects":["Analytic functions; Theta functions; Bargmann functions; Finite quantum systems"],"languages":["en"],"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>."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10454/14366","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Vourdas, Apostolos","Lei, Ci"]},{"key":"dc:creator","label":"Author","values":["Evangelides, Pavlos"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-01-04T16:48:26Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-01-04T16:48:26Z"]},{"key":"dc:date.issued","label":"Date","values":["2015"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Faculty of Engineering and Informatics Department of Computing"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Bradford"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Analytic functions; Theta functions; Bargmann functions; Finite quantum systems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["<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>."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10454/14366"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Analytic representations of quantum systems with Theta functions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Vourdas, Apostolos","Lei, Ci"],"dc:creator":["Evangelides, Pavlos"],"dc:date.accessioned":["2018-01-04T16:48:26Z"],"dc:date.available":["2018-01-04T16:48:26Z"],"dc:date.issued":["2015"],"dc:description.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."],"dc:identifier.uri":["http://hdl.handle.net/10454/14366"],"dc:language.iso":["en"],"dc:publisher.department":["Faculty of Engineering and Informatics Department of Computing"],"dc:publisher.institution":["University of Bradford"],"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>."],"dc:subject":["Analytic functions; Theta functions; Bargmann functions; Finite quantum systems"],"dc:title":["Analytic representations of quantum systems with Theta functions"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-24T01:14:32Z"}