Lyapunov exponents in 1d disordered system with long-range memory
Abstract
The Lyapunov exponents for Anderson localization are studied in a one dimensional disordered system. A random Gaussian potential with the power law decay 1/|x|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.
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