Statistics of Lyapunov exponents of quasi-one-dimensional disordered systems

Statistical properties of Lyapunov exponents (LE) are numerically calculated in a quasi-one-dimensional (1D) Anderson model, which is in a 2D or 3D lattice with a finite cross section. The single-parameter scaling (SPS) variable tau relating the Lyapunov exponents gamma and their variances sigma by tau=sigma L-2/<gamma > is calculated for different lateral coupling t and disorder strength W. In a wide range of t, tau is approximately independent of W, but it has different values for LEs in different channels. For small t, the distribution of the smallest LE is non-Gaussian and tau strongly depends on W, remarkably different from the 1D SPS hypothesis.