Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields

摘要

We study Schroedinger operators with periodic magnetic field in Euclidean2-space, in the case of irrational magnetic flux. Positive measure Cantorspectrum is generically expected in the presence of an electric potential. Weshow that, even without electric potential, the spectrum has positive measureif the magnetic field is a perturbation of a constant one.