Lyapunov exponents in one-dimensional disordered systems with long-range memory

The Lyapunov exponents for Anderson localization are studied in a one-dimensional disordered system. A random Gaussian potential with the power-law decay similar to 1/vertical bar x vertical bar(q) of the correlation function is considered. The exponential growth of the moments of the eigenfunctions and their derivative is obtained. Positive Lyapunov exponents, which determine the asymptotic growth rate, are found.