Correlation functions of the hard-sphere Lorentz model

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Abstract
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.