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Lifshitz tails and localization in the three-dimensional Anderson model
Alexander Elgart
Source: Duke Math. J. Volume 146, Number 2
(2009), 331-360.
Abstract
Consider the three-dimensional Anderson model with a zero mean and bounded independent, identically distributed random potential. Let $\lambda$ be the coupling constant measuring the strength of the disorder, and let $\sigma(E)$ be the self-energy of the model at energy $E$. For any $\epsilon{>}0$ and sufficiently small $\lambda$, we derive almost-sure localization in the band $E\le -\sigma(0)-\lambda^{4-\epsilon}$. In this energy region, we show that the typical correlation length $\xi_E$ behaves roughly as $O\big((|E|-\sigma(E))^{-1/2}\big)$, completing the argument outlined in the preprint of T. Spencer [18]
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1231170943
Digital Object Identifier: doi:10.1215/00127094-2008-068
Mathematical Reviews number (MathSciNet): MR2477764
Zentralblatt MATH identifier: 05501868
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