Abstract
We consider a two dimensional magnetic Schrödinger 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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Communicated by B. Simon
Partially supported by SFB-TR12 of the German Science Foundation.
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Erdős, L., Hasler, D. Wegner Estimate and Anderson Localization for Random Magnetic Fields. Commun. Math. Phys. 309, 507–542 (2012). https://doi.org/10.1007/s00220-011-1373-z
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DOI: https://doi.org/10.1007/s00220-011-1373-z