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.
| Identifer | oai:union.ndltd.org:Potsdam/oai:kobv.de-opus-ubp:5698 |
| Date | January 2012 |
| Creators | Klein, Markus, Rosenberger, Elke |
| Publisher | Universität Potsdam, Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik |
| Source Sets | Potsdam University |
| Language | English |
| Detected Language | English |
| Type | Preprint |
| Format | application/pdf |
| Source | Annales Henri Poincaré, DOI: 10.1007/s00023-011-0152-x |
| Rights | http://opus.kobv.de/ubp/doku/urheberrecht.php |
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