Tunneling for a class of difference operators
- We analyze a general class of difference operators on where is a multi-well potential and is a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schrodinger operator [see Helffer and Sjostrand in Commun Partial Differ Equ 9:337-408, 1984], and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
| Author details: | Markus KleinGND, Elke RosenbergerORCiD |
|---|---|
| DOI: | https://doi.org/10.1007/s00023-011-0152-x |
| ISSN: | 1424-0637 |
| Title of parent work (English): | ANNALES HENRI POINCARE |
| Publisher: | Springer |
| Place of publishing: | Basel |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2012 |
| Publication year: | 2012 |
| Release date: | 2017/03/26 |
| Volume: | 13 |
| Issue: | 5 |
| Number of pages: | 39 |
| First page: | 1231 |
| Last Page: | 1269 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
