Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields

Details Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields

2002-09-19

arxiv.org/abs/math-ph/0209039v1

J. Math. Phys. 44.4 (2003), 1584-1599

Physics

Mathematical Physics

17 pages

Scientific paper

10.1063/1.1556551

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

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