The periodic magnetic Schrödinger operators: spectral gaps and tunneling effect

Details The periodic magnetic Schrödinger operators: spectral gaps and tunneling effect The periodic magnetic Schrödinger operators: spectral gaps and tunneling effect

2007-02-26

arxiv.org/abs/math/0702776v1

Mathematics

Spectral Theory

LaTeX 2e, 12 pages

Scientific paper

A periodic Schr\"odinger 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.

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