Finite-length Lyapunov exponents and conductance for quasi-1D disordered solids

TL;DR

This paper uses the transfer matrix method to analyze finite quasi-1D disordered solids, focusing on Lyapunov exponents and conductance, comparing numerical results with theoretical predictions and exploring finite size effects.

Contribution

It introduces a numerical investigation of finite-length Lyapunov exponents and conductance in quasi-1D disordered systems, highlighting finite size and coupling effects.

Findings

Level spacing distribution for Lyapunov exponents analyzed

Conductance fluctuations characterized for different system sizes

Comparison with scattering matrix results confirms theoretical predictions

Abstract

The transfer matrix method is applied to finite quasi-1D disordered samples attached to perfect leads. The model is described by structured band matrices with random and regular entries. We investigate numerically the level spacing distribution for finite-length Lyapunov exponents as well as the conductance and its fluctuations for different channel numbers and sample sizes. A comparison is made with theoretical predictions and with numerical results recently obtained with the scattering matrix approach. The role of the coupling and finite size effects is also discussed.