Theory of Atomic Motions in Simple Classical Liquids

This paper is an attempt towards developing a theory of the self-motion of atoms in monatomic classical fluids, based on a simplified Liouville equation and on a knowledge of the interaction potential $V(r)$ and the static pair correlation function $g(r)$. A nonlinear integral equation for the velocity autocorrelation function Φ(t) is derived which under certain approximations can be written as dΦ(t)dt+∫0ᵗK(t-t^')Φ(t^')dt^'=0 where the kernel $K(t)$ is an implicit function of Φ(t). An expression for $K(t)$ in terms of $V(r)$ and $g(r)$ has been given. Explicit numerical calculations for the "memory" function $K(t)$ have been made for liquid argon at T=85.9^∘K, and the results have been compared with those obtained by Rahman from his machine computations.