Wegner estimate and Anderson localization for random magnetic fields

Details Wegner estimate and Anderson localization for random magnetic fields Wegner estimate and Anderson localization for random magnetic fields

2010-12-23

arxiv.org/abs/1012.5185v1

Physics

Mathematical Physics

30 pages

Scientific paper

We consider a two dimensional magnetic Schroedinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove the Wegner estimate at arbitrary energy, i.e. we show that the averaged density of states is finite throughout the whole spectrum. We also prove Anderson localization at the bottom of the spectrum.

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