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Semiclassical asymptotics and gaps in the spectra of periodic Schrödinger operators with magnetic wells

Bernard Helffer·Yuri A. Kordyukov
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Abstract

We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schrödinger operator with magnetic wells on a noncompact Riemannian manifold $M$ such that $H^1(M, \R)=0$ equipped with a properly disconnected, cocompact action of a finitely generated, discrete group of isometries has an arbitrarily large number of spectral gaps in the semi-classical limit.

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Bernard Helffer, Yuri A. Kordyukov. 2006-09-13. Semiclassical asymptotics and gaps in the spectra of periodic Schrödinger operators with magnetic wells. https://arxiv.org/abs/math/0601366

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