Finite-Size Corrections in Lyapunov Spectra for Band Random Matrices

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.