Spectral gaps for periodic Schrödinger operators with strong magnetic fields

Abstract

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

14 pages, LaTeX2e, xypic, no figures

References in corpus (2)

• Spectral Gaps for Periodic Elliptic Operators with High Contrast: an Overview
• Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory

Cited by in corpus (1)

• The periodic magnetic Schrödinger operators: spectral gaps and tunneling effect