Localization transition of the three-dimensional 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.