Liquid dynamics theory of the velocity autocorrelation function and self-diffusion

Abstract

In equilibrium liquid dynamics theory, the potential energy surface is supposed to consist of a large number of many-particle nearly harmonic random structural valleys. The passage of the system from one valley to another is a transit, and the transit motion has to be accounted for in order to apply liquid dynamics theory to nonequilibrium processes. The role of transits in liquid dynamics theory is equivalent to the role of collisions in gas dynamics theory. In a classical monatomic liquid, transits are so frequent that each ion ``sees'' a rapidly fluctuating well during one mean vibrational period. This condition is represented approximately by an independent ion model, in which each ion moves in a smooth harmonic well of frequency \ensuremath{\omega}, and at each classical turning point the ion enters a new well with probability \ensuremath{\mu}, or returns in its old well with probability $1\ensuremath{-}\ensuremath{\mu}.$ The corresponding velocity autocorrelation function, which depends on \ensuremath{\omega} and a simple function \ensuremath{\xi}(\ensuremath{\mu}), can be made to fit previously published computer calculations. The frequency \ensuremath{\omega} is close to the mean phonon frequency of the crystalline state, confirming a prediction of equilibrium liquid dynamics theory, and the transit probability \ensuremath{\mu} is around $\frac{1}{2}.$ Analysis of experimental diffusion data suggests that \ensuremath{\xi} is approximately a universal function of ${T/T}_{m}.$