Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials

Details Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials

2010-12-24

arxiv.org/abs/1012.5418v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

18 pages, 11 figures

Scientific paper

Distribution of the transmission coefficient T of a long system with a correlated Gaussian disorder is studied analytically and numerically in terms of the generalized Lyapunov exponent (LE) and the cumulants of lnT. The effect of the disorder correlations on these quantities is considered in weak, moderate and strong disorder for different models of correlation. Scaling relations between the cumulants of lnT are obtained. The cumulants are treated analytically within the semiclassical approximation in strong disorder, and numerically for an arbitrary strength of the disorder. A small correlation scale approximation is developed for calculation of the generalized LE in a general correlated disorder. An essential effect of the disorder correlations on the transmission statistics is found. In particular, obtained relations between the cumulants and between them and the generalized LE show that, beyond weak disorder, transmission fluctuations and deviation of their distribution from the log-normal form (in a long but finite system) are greatly enhanced due to the disorder correlations. Parametric dependence of these effects upon the correlation scale is presented.

Affiliated with

Also associated with

No associations

Rating

Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-643520