Semiclassical spectral analysis of discrete Witten Laplacians

A discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2013

Author dc:creator

• Di Gesù, Giacomo

Contributors dc:contributor

• Klein, Markus

• Semiklassische Spektralasymptotik
• Metastabilität
• diskreter Witten-Laplace-Operator
• Eyring-Kramers Formel
• Tunneleffekt
• semiclassical spectral asymptotics
• metastability
• low-lying eignvalues
• discrete Witten complex
• rescaled lattice

Statement dc:rights

• Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 3.0 Deutschland

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/6287

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:6287