The long time and Brownian limits for tagged particle motion in liquids

Abstract

Formally exact theories of tagged particle motion in liquids are developed, based upon kinetic theory for hard spheres and mode coupling for smooth potentials. It is shown that the resulting equations are tractable in the long time and Brownian limits. The coefficient of the long time tail of the velocity correlation function is seen to differ from its low-density form by only the replacement of the low-density viscosity and diffusion constant by the true viscosity and diffusion constant. In the Brownian limit, the slip Stokes-Einstein law is obtained, with the true viscosity. The relation to other work is discussed.