Fluctuations of the Lyapunov exponent in 2D disordered systems

TL;DR

This paper numerically investigates how the Lyapunov exponent fluctuates in two-dimensional disordered systems, revealing that its mean-to-variance ratio varies but aligns with the single parameter scaling hypothesis.

Contribution

It provides the first detailed numerical analysis of Lyapunov exponent fluctuations in 2D disordered systems, extending understanding beyond 1D cases.

Findings

Mean-to-variance ratio varies in 2D systems

Results support the single parameter scaling hypothesis

Fluctuation behavior differs from 1D systems

Abstract

We report a numerical investigation of the fluctuations of the Lyapunov exponent of a two dimensional non-interacting disordered system. While the ratio of the mean to the variance of the Lyapunov exponent is not constant, as it is in one dimension, its variation is consistent with the single parameter scaling hypothesis.