@phdthesis{Rosenberger2006,
  author    = {Rosenberger, Elke},
  title     = {Asymptotic spectral analysis and tunnelling for a class of difference operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-7393},
  school      = {Universit{\"a}t Potsdam},
  year      = {2006},
  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.},
  subject      = {Mathematische Physik},
  language  = {en}
}