 96303 Barbaroux J.M., Combes J.M., Hislop P.D.
 Localization near band edges for random Schr\"odinger operators
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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 Andersontype
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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