Complex transport in strongly disordered materials

The Lorentz model constitutes a reference model for transport in disordered materials. Here a tracer meanders through an array of frozen obstacles which in the simplest variant are assumed to be distributed independently. As the density of scatterers increases, the regions of excluded volume start to overlap until eventually long-range transport ceases to exist entirely. This localization transition is of purely geometric origin and coincides with the percolation of the void space.