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.

Semiclassical spectral analysis of discrete Witten Laplacians / DI GESU', GIACOMO FILIPPO. - (2013).

Semiclassical spectral analysis of discrete Witten Laplacians

Giacomo Filippo Di Gesu
Primo
2013

Abstract

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.
2013
discrete Witten complex; low-lying eigenvalues; metastability; rescaled lattice; semiclassical spectral asymptotics
03 Monografia::03a Saggio, Trattato Scientifico
Semiclassical spectral analysis of discrete Witten Laplacians / DI GESU', GIACOMO FILIPPO. - (2013).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1691343
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