Geodesic
Lyapunov exponents in 1D Anderson localization with long-range correlations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 297-302

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The Lyapunov exponents for Anderson localization are studied in a one dimensional disordered system. A random Gaussian potential with the power law decay $\sim1/|x|^q$ 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.
Keywords: long-range correlations, fractional derivatives.
Mots-clés : Furutsu–Novikov formula 
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Alexander Iomin. Lyapunov exponents in 1D Anderson localization with long-range correlations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 297-302. http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a3/