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 $\mathbb{Z}$.

8 pages, 1 figure

References in corpus (2)

• Eigenvector localization for random band matrices with power law band width
• Scaling diagram for the localization length at a band edge

Cited by in corpus (1)

• On the Sum of the Non-Negative Lyapunov Exponents for Some Cocycles Related to the Anderson Model