Tunneling for a class of difference operators

  • We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schrödinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.

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Metadaten
Author:Markus Klein, Elke Rosenberger
URN:urn:nbn:de:kobv:517-opus-56989
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1 (2012) 5)
Document Type:Preprint
Language:English
Date of Publication (online):2012/01/06
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/01/06
Tag:interaction matrix; semi-classical difference operator; tunneling
Source:Annales Henri Poincaré, DOI: 10.1007/s00023-011-0152-x
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G99 None of the above, but in this section
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q15 Perturbation theories for operators and differential equations
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q20 Semiclassical techniques, including WKB and Maslov methods
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990 , UK 1200