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.
Semiklassische Spektralasymptotik, Metastabilität, diskreter Witten-Laplace-Operator, Eyring-Kramers Formel, Tunneleffekt, semiclassical spectral asymptotics, metastability, low-lying eignvalues, discrete Witten complex, rescaled lattice
Networked Digital Library of Theses and Dissertations