Localization Transition of the 3D Lorentz Model and Continuum Percolation

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.