Spectral Gaps for Periodic Schrödinger Operators with Strong Magnetic Fields
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- Kordyukov, Y. Commun. Math. Phys. (2005) 253: 371. doi:10.1007/s00220-004-1134-3
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We consider Schrödinger operators Hh=(ih d+A)*(ih d+A) with the periodic magnetic field B=dA on covering spaces of compact manifolds. Using methods of a paper by Kordyukov, Mathai and Shubin , 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.