Spectral gaps for periodic Schrödinger operators with strong magnetic fields

Details Spectral gaps for periodic Schrödinger operators with strong magnetic fields Spectral gaps for periodic Schrödinger operators with strong magnetic fields

2003-11-12

arxiv.org/abs/math/0311200v1

Commun. Math. Phys. 253 (2005), no. 2, 371--384.

Mathematics

Spectral Theory

14 pages, LaTeX2e, xypic, no figures

Scientific paper

We consider Schr\"odinger operators $H^h = (ih d+{\bf A})^* (ih d+{\bf A})$
with the periodic magnetic field ${\bf B}=d{\bf A}$ on covering spaces of
compact manifolds. Under some assumptions on $\bf B$, we prove that there are
arbitrarily large number of gaps in the spectrum of these operators in the
semiclassical limit of strong magnetic field $h\to 0$.

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