96-303 Barbaroux J.M., Combes J.M., Hislop P.D.

Localization near band edges for random Schr\"odinger operators (81K, LaTeX) Jun 18, 96

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Abstract. In this article, we prove exponential localization for wide classes of Schr\"odi-\noindent nger operators, including those with magnetic fields, at the edges of unperturbed spectral gaps. We assume that the unperturbed operator $H_0$ has an open gap $ I_0 \equiv ( B_{-} , B_{+} )$. The random potential is assumed to be Anderson-type with independent, identically distributed coupling constants. The common density may have either bounded or unbounded support. For either case, we prove that there exists an interval of energies in the unperturbed gap for which the almost sure spectrum of the family $H_{ \omega } \equiv H_0 + V_{ \omega }$ is dense pure point with exponentially decaying eigenfunctions. We also prove that the integrated density of states is Lipschitz continuous in the unperturbed spectral gap $ I_0 $.

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