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

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 $<0|P_{[a,b]}e^{-itH}|x>$ 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 08544-0708.