On fluctuations and localization length for the Anderson model on a strip

Abstract

We consider the Anderson model on a strip. Assuming that potentials have bounded density with considerable tails we get a lower bound for the fluctuations of the logarithm of the Green's function in a finite box. This implies an effective estimate by $\exp (C{W}^2)$ for the localization length of the Anderson model on the strip of width $W$. The results are obtained, actually, for a more general model with a non-local operator in the vertical direction.

arXiv comment20 pages; v2: fixed a number of typos and small mistakes, added to the introduction