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Journal of Siberian Federal University. Mathematics & Physics, 2010, Volume 3, Issue 3, Pages 297–302 (Mi jsfu129)  
Lyapunov exponents in 1D Anderson localization with long-range correlations

Alexander Iomin

Department of Physics, Technion, Haifa, Israel
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Abstract: 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, Furutsu–Novikov formula, fractional derivatives.
Received: 10.03.2010
Received in revised form: 10.04.2010
Accepted: 11.06.2010
Document Type: Article
UDC: 538.935
Language: English
Citation: Alexander Iomin, “Lyapunov exponents in 1D Anderson localization with long-range correlations”, J. Sib. Fed. Univ. Math. Phys., 3:3 (2010), 297–302
Citation in format AMSBIB
\Bibitem{Iom10}
\by Alexander~Iomin
\paper Lyapunov exponents in 1D Anderson localization with long-range correlations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2010
\vol 3
\issue 3
\pages 297--302
\mathnet{http://mi.mathnet.ru/jsfu129}
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