The periodic magnetic Schrödinger operators: spectral gaps and tunneling effect

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

A periodic Schrödinger operator on a noncompact Riemannian manifold $M$ such that $H^1(M, \mathbb R)=0$ endowed with a properly discontinuous cocompact isometric action of a discrete group is considered. Under some additional conditions on the magnetic field existence of an arbitrary large number of gaps in the spectrum of such an operator in the semiclassical limit is established. The proofs are based on the study of the tunneling effect in the corresponding quantum system.
LaTeX 2e, 12 pages

Keywords

Spectral Theory, Mathematical Physics

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/124639

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702776
 http://arxiv.org/abs/math/0702776

Collections

arXiv