{"id":{"repo_id":"lethbridge","oai_identifier":"oai:opus.uleth.ca:10133/2490"},"canonical_url":"https://search.dev.ndltd.org/etd/lethbridge/oai:opus.uleth.ca:10133/2490","repository":{"repo_id":"lethbridge","name":"University of Lethbridge","base_url":"https://opus.uleth.ca/server/oai/request"},"display":{"title":"Deformation quantization for contact interactions and dissipation","abstract":"This thesis studies deformation quantization and its application to contact interactions and systems with dissipation. We consider the subtleties related to quantization when contact interactions and boundaries are present. We exploit the idea that discontinuous potentials are idealizations that should be realized as limits of smooth potentials. The Wigner functions are found for the Morse potential and in the proper limit they reduce to the Wigner functions for the infinite wall, for the most general (Robin) boundary conditions. This is possible for a very limited subset of the values of the parameters -- so-called fine tuning is necessary. It explains why Dirichlet boundary conditions are used predominantly. Secondly, we consider deformation quantization in relation to dissipative phenomena. For the damped harmonic oscillator we study a method using a modified noncommutative star product. Within this framework we resolve the non-reality problem with the Wigner function and correct the classical limit.","abstract_html":"This thesis studies deformation quantization and its application to contact interactions and systems with dissipation. We consider the subtleties related to quantization when contact interactions and boundaries are present. We exploit the idea that discontinuous potentials are idealizations that should be realized as limits of smooth potentials. The Wigner functions are found for the Morse potential and in the proper limit they reduce to the Wigner functions for the infinite wall, for the most general (Robin) boundary conditions. This is possible for a very limited subset of the values of the parameters -- so-called fine tuning is necessary. It explains why Dirichlet boundary conditions are used predominantly. Secondly, we consider deformation quantization in relation to dissipative phenomena. For the damped harmonic oscillator we study a method using a modified noncommutative star product. Within this framework we resolve the non-reality problem with the Wigner function and correct the classical limit.","abstract_has_math":false,"creators":["Belchev, Borislav Stefanov","University of Lethbridge. Faculty of Arts and Science"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-27T20:02:35Z","subjects":["Phase space (Statistical physics)","Quantum theory","Dissertations, Academic"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/2490"],"render_values":[{"text":"hdl:10133/2490","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2010"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Phase space (Statistical physics)","Quantum theory","Dissertations, Academic"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/2490"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["This thesis studies deformation quantization and its application to contact interactions and systems with dissipation. We consider the subtleties related to quantization when contact interactions and boundaries are present. We exploit the idea that discontinuous potentials are idealizations that should be realized as limits of smooth potentials. The Wigner functions are found for the Morse potential and in the proper limit they reduce to the Wigner functions for the infinite wall, for the most general (Robin) boundary conditions. This is possible for a very limited subset of the values of the parameters -- so-called fine tuning is necessary. It explains why Dirichlet boundary conditions are used predominantly. Secondly, we consider deformation quantization in relation to dissipative phenomena. For the damped harmonic oscillator we study a method using a modified noncommutative star product. Within this framework we resolve the non-reality problem with the Wigner function and correct the classical limit."]},{"key":"dc:title","label":"Title","values":["Deformation quantization for contact interactions and dissipation"]}]}],"canonical_facts":{"dc:date.issued":["2010"],"dc:description.other":["This thesis studies deformation quantization and its application to contact interactions and systems with dissipation. We consider the subtleties related to quantization when contact interactions and boundaries are present. We exploit the idea that discontinuous potentials are idealizations that should be realized as limits of smooth potentials. The Wigner functions are found for the Morse potential and in the proper limit they reduce to the Wigner functions for the infinite wall, for the most general (Robin) boundary conditions. This is possible for a very limited subset of the values of the parameters -- so-called fine tuning is necessary. It explains why Dirichlet boundary conditions are used predominantly. Secondly, we consider deformation quantization in relation to dissipative phenomena. For the damped harmonic oscillator we study a method using a modified noncommutative star product. Within this framework we resolve the non-reality problem with the Wigner function and correct the classical limit."],"dc:identifier":["hdl:10133/2490"],"dc:subject":["Phase space (Statistical physics)","Quantum theory","Dissertations, Academic"],"dc:title":["Deformation quantization for contact interactions and dissipation"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T20:02:35Z"}