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 $\sim 1/|x{|}^q$ 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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Cited by in corpus (6)

• Localization in one-dimensional chains with Lévy-type disorder
• Localization in fractal and multifractal media
• Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials
• Generalized Lyapunov exponents of the random harmonic oscillator: cumulant expansion approach
• Controlling Anderson localization in disordered heterostructures with Lévy-type distribution
• Localization in a one-dimensional alloy with an arbitrary distribution of spacing between impurities: Application to Lévy glass