, Volume 253, Issue 2, pp 371-384

Spectral Gaps for Periodic Schrödinger Operators with Strong Magnetic Fields

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Abstract

We consider Schrödinger operators H h =(ihd+A)*(ihd+A) with the periodic magnetic field B=d A on covering spaces of compact manifolds. Using methods of a paper by Kordyukov, Mathai and Shubin [14], we prove that, under some assumptions on B, there are in arbitrarily large number of gaps in the spectrum of these operators in the semiclassical limit of the strong magnetic field h→0.

Communicated by B. Simon
Acknowledgement I am very thankful to Bernard Helffer for bringing these problems to my attention and useful discussions and to Mikhail Shubin for his comments.