TY  - JOUR
A1  - Klein, Markus
A1  - Rosenberger, Elke
T1  - Tunneling for a class of difference operators
JF  - ANNALES HENRI POINCARE
N2  - 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.
Y1  - 2012
U6  - https://doi.org/10.1007/s00023-011-0152-x
SN  - 1424-0637
VL  - 13
IS  - 5
SP  - 1231
EP  - 1269
PB  - Springer
CY  - Basel
ER  -