Finite-size corrections to 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 entire Lyapunov spectra of finite samples as a function of the bandwidth and of the sample length. Different scaling laws are found with respect to what is suggested by the analysis of the localization properties of the eigenfunctions. Our results, at variance with the Anderson model, suggest that the contacts of a finite sample with the leads play a prominent role.