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

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

2006-01-15

arxiv.org/abs/math/0601366v2

Mathematics

Spectral Theory

LaTeX 2e, 16 pages

Scientific paper

We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schr\"odinger 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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