Article,
Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation
Physical Review Letters, (2006)
DOI: 10.1103/physrevlett.96.165901
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.
