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

TL;DR

This paper establishes an explicit lower bound for the sum of non-negative Lyapunov exponents in certain cocycles related to the Anderson model, supporting conjectures about their behavior as the system width increases.

Contribution

It provides a new explicit lower bound for the sum of Lyapunov exponents in the Anderson model, aligning with conjectured bounds for the lowest exponent.

Findings

Lower bound proportional to W^{-psilon} for the sum of exponents

Supports conjecture that the lowest Lyapunov exponent is bounded below by W^{-1}

Results are consistent with theoretical predictions for the Anderson model

Abstract

We provide an explicit lower bound for the the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model. In particular, for the Anderson model on a strip of width $ W $ the lower bound is proportional to $ W^{-\epsilon} $, for any $ \epsilon>0 $. This bound is consistent with the fact that the lowest non-negative Lyapunov exponent is conjectured to have a lower bound proportional to $ W^{-1} $.