Scaling properties of Lyapunov spectra for the band random matrix model

The transfer-matrix method is applied to quasi-one-dimensional disordered media described by a one-dimensional tight-binding Hamiltonian with long-range random interactions. We investigate the scaling properties of the whole Lyapunov spectrum in the limit of the interaction range b tending to infinity. Two different energy dependencies are found around the maximum and the minimum Lyapunov exponents. Moreover, a singular behavior in the lower part of the Lyapunov spectrum is found at the band edge. Finally, scaling properties of the fluctuations are also analyzed.