Correlated Motions in Simple Classical Liquids

This paper reports a method for studying correlation functions for simple classical liquids. One atom of the liquid is considered to be an external agent acting on the others, and Liouville's equation is formally solved to obtain their response. From this solution an equation for the velocity autocorrelation function is derived. The method is also applied to the distinct-particle part of the density-density correlation function, $G_d(\overrightarrow{\mathrm{x}}, t)$. The moment relations for $G_d(\overrightarrow{\mathrm{x}}, t)$ are in this way made to depend on a hierarchy of equations relating the static correlation functions. When the basic equations derived by this method are approximated further, previously given approximations for $G_d(\overrightarrow{\mathrm{x}}, t)$ are obtained.