A lower bound for the Lyapounov exponents of the random Schrodinger operator on a strip

Abstract

We consider the random Schrodinger 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 \(-W\) or \(W\to \infty\). 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 RSO theory on \(\mathbb Z\).