The Periodic Magnetic Schrödinger Operators: Spectral Gaps and Tunneling Effect
نویسنده
چکیده
A periodic Schrödinger operator on a noncompact Riemannian manifold M such that H1(M, R) = 0 endowed with a properly discontinuous cocompact isometric action of a discrete group are 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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