Conference paper
Authors list: Kantelhardt, JW; Bunde, A
Publication year: 1998
Pages: 400-405
Journal: Annalen der Physik
Volume number: 7
Issue number: 5-6
ISSN: 0003-3804
eISSN: 1521-3889
DOI Link: https://doi.org/10.1002/andp.199851005-607
Conference: 210 WE-Heraeus-Seminar on Percolation, Interaction, Localization - Simulations of Transport in Disordered Systems
Publisher: Wiley
Abstract:
We compare numerically the localization behavior of electronic eigenfunctions in the Anderson model and on self-similar percolation clusters at criticality. We find that the distributions of the local wave function amplitudes \psi\ at fixed distances from the localization center are very similar for both models; The amplitude distributions are well approximated by log-normal fits, which seem to become exact at large distances. From the distributions, we can calculate analytically the behavior of the averages at sufficiently large distances. We observe two different localization regimes. In the first regime, at intermediate distances from the localization center, we find stretched exponential localization ('sublocalization'), ln[\psi\] similar to -r(d psi), with effective localization exponents d(psi) < 1. In the second regime, for very large r, the averages strongly depend on the number of configurations N, and superlocalization (d(psi) > 1) is observed, converging to simple exponential behavior asymptotically as expected. The crossover from the intermediate to the asymptotic regime depends logarithmically on the number of configurations.
Citation Styles
Harvard Citation style: Kantelhardt, J. and Bunde, A. (1998) Wave functions in the Anderson model and in the quantum percolation model: a comparison, Annalen der Physik, 7(5-6), pp. 400-405. https://doi.org/10.1002/andp.199851005-607
APA Citation style: Kantelhardt, J., & Bunde, A. (1998). Wave functions in the Anderson model and in the quantum percolation model: a comparison. Annalen der Physik. 7(5-6), 400-405. https://doi.org/10.1002/andp.199851005-607
