A Lower Bound for the Lyapounov Exponents of the Random Schrödinger Operator on a Strip

Abstract

We consider the random Schrödinger operator on a strip of width W, assuming the site distribution of bounded density. It is shown that the positive Lyapounov exponents satisfy a lower bound roughly exponential in −W for W→∞. The argument proceeds directly by establishing Green’s function decay, but does not appeal to Furstenberg’s random matrix theory on the strip. One ingredient involved is the construction of ‘barriers’ using the random Schrödinger operator theory on $\mathbb{Z}$ .