01-358 Frederic Klopp

Weak disorder localization and Lifshitz tails: continuous Hamiltonians (361K, Postscript) Oct 8, 01

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Abstract. This paper is devoted to the study of band edge localization for continuous random Schr dinger operators with weak random perturbations. We prove that, in the weak disorder regime, $\lambda$ small, the spectrum in intervals of size $\lambda$ at a non-degenerate simple band edge is exponentially and dynamically localized. Upper bounds on the localization length in these energy regions are also obtained. Our results rely on the analysis of Lifshitz tails when the disorder is small; the single site potential need not be of fixed sign.

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