Velocity Correlation Functions in Two and Three Dimensions

Velocity correlation functions ρ(t) in hard-disk and hard-sphere fluids are discussed on the basis of the kinetic theory of gases. It is found in d dimensions that ρ(t)~α(tt₀)^-d/2 with α=O(ρ^d-1) (t₀^-1=collisionfrequency; ρ=reduceddensity). Expressions for α are given that seem correct at low densities and a good approximation at least up to half the close-packing density. The agreement with Alder and Wainwright's computer results is good.