Frederic Klopp
Weak disorder localization and Lifshitz tails
(393K, Postscript)
ABSTRACT. This paper is devoted to the study of localization of discrete
random Schr dinger Hamiltonians in the weak disorder regime.
Consider an i.i.d. Anderson model and assume that its left spectral
edge is 0. Let $\gamma$ be the coupling constant measuring the
strength of the disorder. For $\gamma$ small, we prove a Lifshitz
tail type estimate and use it to derive localization in a band
starting at 0 going up to a distance $\gamma^{1+\eta}$
($0<\eta<\eta_0$) of the average of the potential. In this energy
region, we show that the localization length at energy $E$ is
bounded from above by a constant times the square root of the
distance between $E$ and the average of the potential.