 93282 Michael Aizenman
 Localization at Weak Disorder: Some Elementary Bounds
(175K, RTF)
Oct 28, 93

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Abstract. An elementary proof is given of localization for linear operators
$H=H_0+\lambda V$, with $H_0$ translation invariant, or periodic, and
$V(\cdot)$ a random potential, in energy regimes which for weak
disorder $(\lambda \to 0)$ are close to the unperturbed spectrum
($\sigma (H_0)$). The analysis is within the approach introduced in
the recent study of localization at high disorder by Aizenman and
Molchanov [AM]; the localization regimes discussed in the two works
being supplementary. Included also are some general auxiliary results
enhancing the method, which now yields uniform exponential decay for
the matrix elements $<0P_{[a,b]}e^{itH}x>$ of the spectrally
filtered unitary time evolution operators, with $[a,b]$ in the
relevant energy range.
The article is archived in the RTF format. If you would
rather have a hard copy, send a request to: aizenman@princeton.edu
or: M. Aizenman, Jadwin Hall, P.O.Box 708, Princeton, NY 085440708.
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