Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model

Details Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model

2002-01-20

arxiv.org/abs/cond-mat/0201356v2

Phys. Rev. B 66, 035118 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages with 9 figures and 1 table

Scientific paper

10.1103/PhysRevB.66.035118

We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed distances from the localization center are well approximated by log-normal fits which become exact at large distances. These fits are consistent with the standard single parameter scaling theory for the Anderson model in 1d, but they suggest that a second parameter is required to describe the scaling behavior of the amplitude fluctuations in 2d. From the log-normal distributions we calculate analytically the decay of the mean wave functions. For short distances from the localization center we find stretched exponential localization ("sublocalization") in both, 1d and 2d. In 1d, for large distances, the mean wave functions depend on the number of configurations N used in the averaging procedure and decay faster that exponentially ("superlocalization") converging to simple exponential behavior only in the asymptotic limit. In 2d, in contrast, the localization length increases logarithmically with the distance from the localization center and sublocalization occurs also in the second regime. The N-dependence of the mean wave functions is weak. The analytical result agrees remarkably well with the numerical calculations.

Affiliated with

Also associated with

No associations

Rating

Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model 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 Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-665950