Abstract
We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erdős and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis.
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Partially supported by SFB-TR12 of the German Science Foundation.
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Erdős, L., Hasler, D. Anderson Localization at Band Edges for Random Magnetic Fields. J Stat Phys 146, 900–923 (2012). https://doi.org/10.1007/s10955-012-0445-6
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DOI: https://doi.org/10.1007/s10955-012-0445-6