Finite-Size Corrections in Lyapunov Spectra for Band Random Matrices

TL;DR

This paper studies how the Lyapunov spectra of band random matrices in disordered systems converge with finite size, revealing different scaling laws at spectrum edges.

Contribution

It introduces finite-size correction analysis for Lyapunov spectra in band random matrices, highlighting distinct scaling behaviors at spectrum extremities.

Findings

Different scaling laws at maximal and minimal Lyapunov exponents

Convergence properties depend on bandwidth and sample length

Insights into spectral stability in disordered systems

Abstract

The transfer matrix method is applied to quasi one-dimensional and one-dimensional disordered systems with long-range interactions, described by band random matrices. We investigate the convergence properties of the whole Lyapunov spectra of finite samples as a function of the bandwidth and of the sample length. Two different scaling laws are found at the maximal and minimal Lyapunov exponents.