Fully Renormalized Kinetic Theory. I. Self-Diffusion

Abstract

In this paper a new fully renormalized kinetic theory for self-diffusion is described. The theory is developed in terms of time-dependent correlation functions, and the main effort is in deriving general microscopic expressions for the memory function associated with the phase-space fluctuation function. These general expressions are valid for all frequencies and wave numbers and are rearranged in a way such that approximations can be made at a microscopic level in a straightforward manner. The main idea in the rearrangement is the expression of the memory function in terms of an effective two-body problem where the dynamics are described by the two-particle Liouville operator and an effective source representing the effect of the other $N-2$ particles in the system on the colliding pair. An exact microscopic expression for the two-particle source is derived. It is shown that even the simplest approximation in this scheme leads to the nontrivial Boltzmann-Enskog approximation for the memory function.