Asymptotic spectral analysis and tunnelling for a class of difference operators

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2006

Author dc:creator

• Rosenberger, Elke

Contributors dc:contributor

• Klein, Markus

• Semi-klasische Abschätzung
• Finsler-Abstand
• Pseudodifferentialoperatoren auf dem Torus
• Kontinuumsgrenzwert
• Differenzenoperator
• tunneling
• semi-classical spectral estimates
• Finsler-distance
• difference operator
• scaled lattice

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/658

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:658