arXiv 0801.44602008-01-29math.SPmath-phmath.MP

Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells

Bernard Helffer, Yuri A. Kordyukov

备注：: 16 pages

英文摘要：

We consider a periodic magnetic Schrödinger operator on a noncompact Riemannian manifold $M$ such that $H^1(M, \RR)=0$ endowed with a properly discontinuous cocompact isometric action of a discrete group. We assume that there is no electric field and that the magnetic field has a periodic set of compact magnetic wells. We review a general scheme of a proof of existence of an arbitrary large number of gaps in the spectrum of such an operator in the semiclassical limit, which was suggested in our previous paper, and some applications of this scheme. Then we apply these methods to establish similar results in the case when the wells have regular hypersurface pieces.

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