{"id":{"repo_id":"potsdam-diss","oai_identifier":"oai:kobv.de-opus4-uni-potsdam:658"},"canonical_url":"https://search.dev.ndltd.org/etd/potsdam-diss/oai:kobv.de-opus4-uni-potsdam:658","repository":{"repo_id":"potsdam-diss","name":"Universität Potsdam - Diss","base_url":"https://publishup.uni-potsdam.de/opus4-ubp/oai"},"display":{"title":"Asymptotic spectral analysis and tunnelling for a class of difference operators","abstract":"We analyze the asymptotic behavior in the limit epsilon to zero for a wide class of difference operators H_epsilon = T_epsilon + V_epsilon with underlying multi-well potential. They act on the square summable functions on the lattice (epsilon Z)^d. We start showing the validity of an harmonic approximation and construct WKB-solutions at the wells. Then we construct a Finslerian distance d induced by H and show that short integral curves are geodesics and d gives the rate for the exponential decay of Dirichlet eigenfunctions. In terms of this distance, we give sharp estimates for the interaction between the wells and construct the interaction matrix.","abstract_html":"We analyze the asymptotic behavior in the limit epsilon to zero for a wide class of difference operators H_epsilon = T_epsilon + V_epsilon with underlying multi-well potential. They act on the square summable functions on the lattice (epsilon Z)^d. We start showing the validity of an harmonic approximation and construct WKB-solutions at the wells. Then we construct a Finslerian distance d induced by H and show that short integral curves are geodesics and d gives the rate for the exponential decay of Dirichlet eigenfunctions. In terms of this distance, we give sharp estimates for the interaction between the wells and construct the interaction matrix.","abstract_has_math":false,"creators":["Rosenberger, Elke"],"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":2006,"date_issued":"2006-05-26","date_published":"2006-05-26","updated_at":"2026-07-24T03:51:16Z","subjects":["Semi-klasische Abschätzung","Finsler-Abstand","Pseudodifferentialoperatoren auf dem Torus","Kontinuumsgrenzwert","Differenzenoperator","tunneling","semi-classical spectral estimates","Finsler-distance","difference operator","scaled lattice"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://publishup.uni-potsdam.de/frontdoor/index/index/docId/658","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":["Rosenberger, Elke"]}]},{"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":["Semi-klasische Abschätzung","Finsler-Abstand","Pseudodifferentialoperatoren auf dem Torus","Kontinuumsgrenzwert","Differenzenoperator","tunneling","semi-classical spectral estimates","Finsler-distance","difference operator","scaled lattice"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We analyze the asymptotic behavior in the limit epsilon to zero for a wide class of difference operators H_epsilon = T_epsilon + V_epsilon with underlying multi-well potential. They act on the square summable functions on the lattice (epsilon Z)^d. We start showing the validity of an harmonic approximation and construct WKB-solutions at the wells. Then we construct a Finslerian distance d induced by H and show that short integral curves are geodesics and d gives the rate for the exponential decay of Dirichlet eigenfunctions. In terms of this distance, we give sharp estimates for the interaction between the wells and construct the interaction matrix.","Wir analysieren das asymptotische Verhalten im Grenzwert epsilon gegen null von einer weiten Klasse von Differenzen operatoren H_epsilon = T_epsilon + V_epsilon mit unterliegendem Potential. Sie wirken auf die quadrat-summierbaren Funktionen auf dem Gitter (epsilon Z)^d. Zunächst zeigen wir die Gültigkeit einer harmonischen Approximation und konstruieren WKB-Lösungen an den Töpfen. Dann konstruieren wir eine Finslersche Abstandsfunktion d, die durch H induziert wird und zeigen, daß kurze Integralkurven Geodäten sind und daß d die Rate des exponentiellen Abfallverhaltens von Dirichlet-Eigenfunktionen beschreibt. Bezügliche dieses Abstands geben wir scharfe Abschätzungen für die Wechselwirkung zwischen den Töpfen und konstruieren die Wechselwirkungs-Matrix."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Asymptotic spectral analysis and tunnelling for a class of difference operators","Asymptotische Spektralanalyse und Tunneleffekt für eine Klasse von Differenzen-Operatoren"]}]}],"canonical_facts":{"dc:contributor":["Klein, Markus"],"dc:creator":["Rosenberger, Elke"],"dc:description.abstract":["We analyze the asymptotic behavior in the limit epsilon to zero for a wide class of difference operators H_epsilon = T_epsilon + V_epsilon with underlying multi-well potential. They act on the square summable functions on the lattice (epsilon Z)^d. We start showing the validity of an harmonic approximation and construct WKB-solutions at the wells. Then we construct a Finslerian distance d induced by H and show that short integral curves are geodesics and d gives the rate for the exponential decay of Dirichlet eigenfunctions. In terms of this distance, we give sharp estimates for the interaction between the wells and construct the interaction matrix.","Wir analysieren das asymptotische Verhalten im Grenzwert epsilon gegen null von einer weiten Klasse von Differenzen operatoren H_epsilon = T_epsilon + V_epsilon mit unterliegendem Potential. Sie wirken auf die quadrat-summierbaren Funktionen auf dem Gitter (epsilon Z)^d. Zunächst zeigen wir die Gültigkeit einer harmonischen Approximation und konstruieren WKB-Lösungen an den Töpfen. Dann konstruieren wir eine Finslersche Abstandsfunktion d, die durch H induziert wird und zeigen, daß kurze Integralkurven Geodäten sind und daß d die Rate des exponentiellen Abfallverhaltens von Dirichlet-Eigenfunktionen beschreibt. Bezügliche dieses Abstands geben wir scharfe Abschätzungen für die Wechselwirkung zwischen den Töpfen und konstruieren die Wechselwirkungs-Matrix."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Potsdam"],"dc:subject":["Semi-klasische Abschätzung","Finsler-Abstand","Pseudodifferentialoperatoren auf dem Torus","Kontinuumsgrenzwert","Differenzenoperator","tunneling","semi-classical spectral estimates","Finsler-distance","difference operator","scaled lattice"],"dc:title":["Asymptotic spectral analysis and tunnelling for a class of difference operators","Asymptotische Spektralanalyse und Tunneleffekt für eine Klasse von Differenzen-Operatoren"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Potsdam"]},"updated_at":"2026-07-24T03:51:16Z"}