Lyapunov exponents in 1D Anderson localization with long-range correlations

Alexander Iomin

Department of Physics, Technion, Haifa, Israel

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.

UDC: 538.935

Received: 10.03.2010
Received in revised form: 10.04.2010
Accepted: 11.06.2010

Language: English