Self-Diffusion Model for Memory Functions in Classical Fluids

Abstract

The Mori memory-function formalism is used to derive systematically a hierarchy of approximations relating the dynamic structure factor $S(k,\omega )$ of a dense classical fluid to its self-part $S_s(k,\omega )$. The formalism is applied to a column vector of dynamical variables whose components include the self and distinct parts, ${\rho }_s$ and ${\rho }_d$, of the fluctuating density plus $N$ time derivatives of these variables. Increasing $N$ is analogous to a continued-fraction expansion of the memory functions, and builds in more short-time information about the correlation functions. In this manner approximations generated earlier by Vineyard, by Kerr, and by Ortoleva and Nelkin are concisely stated, and a new approximation which gives the first six frequency moments of $S(k,\omega )$ correctly is obtained. Since the sixth frequency moment of $S(k,\omega )$ is not known from molecular-dynamics calculations, it is used as a parameter to fit these calculations. Agreement for $S(k,\omega )$ to within a few percent is obtained for several $k$ values and two thermo-dynamic states. The deduced value of the sixth frequency moment has a reasonable dependence on $k$, and may give useful information about the three-particle static correlation function.