{"id":{"repo_id":"potsdam-diss","oai_identifier":"oai:kobv.de-opus4-uni-potsdam:6287"},"canonical_url":"https://search.dev.ndltd.org/etd/potsdam-diss/oai:kobv.de-opus4-uni-potsdam:6287","repository":{"repo_id":"potsdam-diss","name":"Universität Potsdam - Diss","base_url":"https://publishup.uni-potsdam.de/opus4-ubp/oai"},"display":{"title":"Semiclassical spectral analysis of discrete Witten Laplacians","abstract":"A discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice.","abstract_html":"A discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice.","abstract_has_math":false,"creators":["Di Gesù, Giacomo"],"institution":"Universität Potsdam","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Klein, Markus"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-04-26","date_published":"2013-04-26","updated_at":"2026-07-24T03:51:43Z","subjects":["Semiklassische Spektralasymptotik","Metastabilität","diskreter Witten-Laplace-Operator","Eyring-Kramers Formel","Tunneleffekt","semiclassical spectral asymptotics","metastability","low-lying eignvalues","discrete Witten complex","rescaled lattice"],"languages":[],"rights":["Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 3.0 Deutschland"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://publishup.uni-potsdam.de/frontdoor/index/index/docId/6287","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Klein, Markus"]},{"key":"dc:creator","label":"Author","values":["Di Gesù, Giacomo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Potsdam"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Potsdam"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Semiklassische Spektralasymptotik","Metastabilität","diskreter Witten-Laplace-Operator","Eyring-Kramers Formel","Tunneleffekt","semiclassical spectral asymptotics","metastability","low-lying eignvalues","discrete Witten complex","rescaled lattice"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 3.0 Deutschland"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice.","In dieser Arbeit wird auf dem n-dimensionalen Gitter der ganzen Zahlen ein Analogon des Witten-Laplace-Operatoren eingeführt. Nach geeigneter Skalierung des Gitters und des Operatoren analysieren wir den Tunneleffekt zwischen verschiedenen Potentialtöpfen und erhalten vollständige Aymptotiken für das tiefliegende Spektrum. Der Beweis (nach Methoden, die von B. Helffer, M. Klein und F. Nier im Falle des kontinuierlichen Witten-Laplace-Operatoren entwickelt wurden) basiert auf der Konstruktion eines diskreten Witten-Komplexes und der Analyse des zugehörigen Witten-Laplace-Operatoren auf 1-Formen. Das Resultat kann im Kontext von metastabilen Markov Prozessen auf dem Gitter reformuliert werden und ermöglicht scharfe Aussagen über metastabile Austrittszeiten."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Semiclassical spectral analysis of discrete Witten Laplacians","Semiklassische Spektraltheorie von diskreten Witten-Laplace-Operatoren"]}]}],"canonical_facts":{"dc:contributor":["Klein, Markus"],"dc:creator":["Di Gesù, Giacomo"],"dc:description.abstract":["A discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice.","In dieser Arbeit wird auf dem n-dimensionalen Gitter der ganzen Zahlen ein Analogon des Witten-Laplace-Operatoren eingeführt. Nach geeigneter Skalierung des Gitters und des Operatoren analysieren wir den Tunneleffekt zwischen verschiedenen Potentialtöpfen und erhalten vollständige Aymptotiken für das tiefliegende Spektrum. Der Beweis (nach Methoden, die von B. Helffer, M. Klein und F. Nier im Falle des kontinuierlichen Witten-Laplace-Operatoren entwickelt wurden) basiert auf der Konstruktion eines diskreten Witten-Komplexes und der Analyse des zugehörigen Witten-Laplace-Operatoren auf 1-Formen. Das Resultat kann im Kontext von metastabilen Markov Prozessen auf dem Gitter reformuliert werden und ermöglicht scharfe Aussagen über metastabile Austrittszeiten."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Potsdam"],"dc:rights":["Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 3.0 Deutschland"],"dc:subject":["Semiklassische Spektralasymptotik","Metastabilität","diskreter Witten-Laplace-Operator","Eyring-Kramers Formel","Tunneleffekt","semiclassical spectral asymptotics","metastability","low-lying eignvalues","discrete Witten complex","rescaled lattice"],"dc:title":["Semiclassical spectral analysis of discrete Witten Laplacians","Semiklassische Spektraltheorie von diskreten Witten-Laplace-Operatoren"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Potsdam"]},"updated_at":"2026-07-24T03:51:43Z"}