Correlation functions of the hard-sphere Lorentz model

Quantitative results for the correlation functions for the Lorentz model of overlapping hard spheres are worked out and discussed within the recently proposed theory of diffusion and localization of a classical particle moving in a random static field. The applicability of the theory to the diffusion phase is established by a successful comparison of the diffusivity as a function of density and the velocity-autocorrelation function as a function of time for various densities, with the computer simulation results of Bruin. Specific predictions of the localization length as a function of density, of a nonmonotonic density dependence of the effective power-law exponent of the long-time tail of the velocity correlations, and of an oscillatory wave-number dependence of the normalized width of van Hove's scattering function are presented.