Simple model for density of states and mobility of an electron in a gas of hard-core scatterers

We give a semiquantitative model for the density of states and transport properties of an electron in a system of randomly located hard-core scatterers. Our main results are these: (a) The density of states has the usual square-root behavior for high energies and a tail of localized states at the low-energy end; the energy at which the transition occurs is computed from percolation theory. (b) For a fixed temperature the fraction of electrons in localized states increases drastically with the density of scatterers above a critical density. Thus, our model provides a physical explanation for the mobility transition found by Neustadter and Coopersmith.