93-282 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 $<0|P_{[a,b]}e^{-itH}|x>$ 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.

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