The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory and obtain an excellent matching of the critical density and exponents. Within a dynamic scaling ansatz incorporating two divergent length scales we achieve data collapse for the mean-square displacements and identify the leading corrections to scaling. We provide evidence for a divergent non-Gaussian parameter close to the transition.
%0 Journal Article
%1 Hofling2006Localization
%A Hofling, Felix
%A Franosch, Thomas
%A Frey, Erwin
%D 2006
%I APS
%J Physical Review Letters
%K localization\_transition, lorentz\_model, msd, percolation lattice-models
%N 16
%R 10.1103/physrevlett.96.165901
%T Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation
%U http://dx.doi.org/10.1103/physrevlett.96.165901
%V 96
%X The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory and obtain an excellent matching of the critical density and exponents. Within a dynamic scaling ansatz incorporating two divergent length scales we achieve data collapse for the mean-square displacements and identify the leading corrections to scaling. We provide evidence for a divergent non-Gaussian parameter close to the transition.
@article{Hofling2006Localization,
abstract = {{The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory and obtain an excellent matching of the critical density and exponents. Within a dynamic scaling ansatz incorporating two divergent length scales we achieve data collapse for the mean-square displacements and identify the leading corrections to scaling. We provide evidence for a divergent non-Gaussian parameter close to the transition.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Hofling, Felix and Franosch, Thomas and Frey, Erwin},
biburl = {https://www.bibsonomy.org/bibtex/2f4b71103b1c4fdc8c31df2a9cda962c5/nonancourt},
citeulike-article-id = {1252079},
citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PRLTAO000096000016165901000001\&idtype=cvips\&gifs=yes},
citeulike-linkout-1 = {http://link.aps.org/abstract/PRL/v96/e165901},
citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevlett.96.165901},
doi = {10.1103/physrevlett.96.165901},
interhash = {42f2425a9e32e930e974ffbb2e30ca75},
intrahash = {f4b71103b1c4fdc8c31df2a9cda962c5},
journal = {Physical Review Letters},
keywords = {localization\_transition, lorentz\_model, msd, percolation lattice-models},
number = 16,
posted-at = {2009-02-18 13:38:39},
priority = {2},
publisher = {APS},
timestamp = {2019-08-01T15:36:09.000+0200},
title = {{Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation}},
url = {http://dx.doi.org/10.1103/physrevlett.96.165901},
volume = 96,
year = 2006
}