Splitting of the Landau levels by magnetic perturbations and Anderson transition in 2D-random magnetic media

Details Splitting of the Landau levels by magnetic perturbations and Anderson transition in 2D-random magnetic media Splitting of the Landau levels by magnetic perturbations and Anderson transition in 2D-random magnetic media

2010-05-17

arxiv.org/abs/1005.2789v2

Mathematics

Spectral Theory

14 pages; remarks added, typos corrected

Scientific paper

In this note we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical delocalization near the center of the bands in the sense that wave packets travel at least at a given minimum speed. We provide explicit examples of magnetic perturbations that split the Landau levels into full intervals of spectrum.

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