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

2006/01/15 by Helffer, Bernard, Kordyukov, Yuri A.
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.math/0601366

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 H¹(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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