{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:63199"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:63199","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"The functional renormalization group for zero-dimensional quantum systems in and out of equilibrium","abstract":"We study transport properties of quantum impurity systems using the functional renormalization group. The latter is an RG-based diagrammatic tool to treat Coulomb interactions in a fast and flexible way. Prior applications, which employed a simple first-order (Hartree-Fock-like) scheme to truncate the FRG flow equations within the Matsubara formalism, succeeded in accurately describing linear transport of various quantum dot geometries at zero temperature T=0. In a nutshell, advance in this Thesis is three-fold. First, we introduce a frequency-dependent second-order approximation in order to eventually compute finite-energy properties such as the conductance at T>0 (mainly focusing on the single impurity Anderson model). Second, a generalisation of the Hartree-Fock-like approach to Keldysh space allows for addressing the non-equilibrium steady-state dynamics of the interacting resonant level model. Third, we investigate the physics of a quantum dot Josephson junction as well as the charging of a single narrow level using the first-order scheme.","abstract_html":"We study transport properties of quantum impurity systems using the functional renormalization group. The latter is an RG-based diagrammatic tool to treat Coulomb interactions in a fast and flexible way. Prior applications, which employed a simple first-order (Hartree-Fock-like) scheme to truncate the FRG flow equations within the Matsubara formalism, succeeded in accurately describing linear transport of various quantum dot geometries at zero temperature T=0. In a nutshell, advance in this Thesis is three-fold. First, we introduce a frequency-dependent second-order approximation in order to eventually compute finite-energy properties such as the conductance at T>0 (mainly focusing on the single impurity Anderson model). Second, a generalisation of the Hartree-Fock-like approach to Keldysh space allows for addressing the non-equilibrium steady-state dynamics of the interacting resonant level model. Third, we investigate the physics of a quantum dot Josephson junction as well as the charging of a single narrow level using the first-order scheme.","abstract_has_math":false,"creators":["Karrasch, Christoph"],"institution":"Publikationsserver der RWTH Aachen University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Meden, Volker"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-30T19:43:35Z","subjects":["info:eu-repo/classification/ddc/530","Renormierungsgruppe","Quantenpunkt","Nichtgleichgewicht","Physik","functional","renormalization","quantum-dot","non-equilibrium","transport"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124646%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124646%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124646%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/63199","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Meden, Volker"]},{"key":"dc:creator","label":"Author","values":["Karrasch, Christoph"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2010"]},{"key":"dc:publisher","label":"Institution","values":["Publikationsserver der RWTH Aachen University"]},{"key":"dc:relation","label":"Dc Relation","values":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-33468"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["info:eu-repo/classification/ddc/530","Renormierungsgruppe","Quantenpunkt","Nichtgleichgewicht","Physik","functional","renormalization","quantum-dot","non-equilibrium","transport"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/record/63199","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124646%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We study transport properties of quantum impurity systems using the functional renormalization group. The latter is an RG-based diagrammatic tool to treat Coulomb interactions in a fast and flexible way. Prior applications, which employed a simple first-order (Hartree-Fock-like) scheme to truncate the FRG flow equations within the Matsubara formalism, succeeded in accurately describing linear transport of various quantum dot geometries at zero temperature T=0. In a nutshell, advance in this Thesis is three-fold. First, we introduce a frequency-dependent second-order approximation in order to eventually compute finite-energy properties such as the conductance at T>0 (mainly focusing on the single impurity Anderson model). Second, a generalisation of the Hartree-Fock-like approach to Keldysh space allows for addressing the non-equilibrium steady-state dynamics of the interacting resonant level model. Third, we investigate the physics of a quantum dot Josephson junction as well as the charging of a single narrow level using the first-order scheme."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University 219 S. : Ill., graph. Darst. (2010). = Aachen, Techn. Hochsch., Diss., 2010"]},{"key":"dc:title","label":"Title","values":["The functional renormalization group for zero-dimensional quantum systems in and out of equilibrium"]}]}],"canonical_facts":{"dc:contributor":["Meden, Volker"],"dc:coverage":["DE"],"dc:creator":["Karrasch, Christoph"],"dc:date":["2010"],"dc:description":["We study transport properties of quantum impurity systems using the functional renormalization group. The latter is an RG-based diagrammatic tool to treat Coulomb interactions in a fast and flexible way. Prior applications, which employed a simple first-order (Hartree-Fock-like) scheme to truncate the FRG flow equations within the Matsubara formalism, succeeded in accurately describing linear transport of various quantum dot geometries at zero temperature T=0. In a nutshell, advance in this Thesis is three-fold. First, we introduce a frequency-dependent second-order approximation in order to eventually compute finite-energy properties such as the conductance at T>0 (mainly focusing on the single impurity Anderson model). Second, a generalisation of the Hartree-Fock-like approach to Keldysh space allows for addressing the non-equilibrium steady-state dynamics of the interacting resonant level model. 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Hochsch., Diss., 2010"],"dc:subject":["info:eu-repo/classification/ddc/530","Renormierungsgruppe","Quantenpunkt","Nichtgleichgewicht","Physik","functional","renormalization","quantum-dot","non-equilibrium","transport"],"dc:title":["The functional renormalization group for zero-dimensional quantum systems in and out of equilibrium"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:43:35Z"}