Velocity-Correlation Functions in Two and Three Dimensions: Low Density

The long-time behavior of velocity-correlation functions ^ (d) (t) characteristic for self-diffusion, viscosity, and heat conductivity is calculated for a gas of hard disks or hard spheres on the basis of the kinetic theory of dense gases. In d dimensions one finds that ^ (d) (t), after an initial exponential decay for a few mean free times t₀, exhibits for times up to at least 40t₀ a decay ^ (d) () ({t₀t) }^d{2}, where ^ (d) is of the order of ^d-1, =na^d with n the number density, and a the hard-disk or hard-sphere diameter. The ^ (d) () are determined by the same dynamical events that are responsible for the divergences in the virial expansion of the transport coefficients. In this paper the ^ (d) () are calculated to lowest order in. In this order, they are identical to the low-density limit of the ^ (d) () that have been obtained by other authors on the basis of hydrodynamical considerations.