Random Events in a Liquid

Abstract

A model is suggested for the evaluation of the time integral of the autocorrelation function for inter-molecular forces. This integral plays the part of a ``friction constant'' in the statistical mechanical theory of transport processes. A cluster of a small number of molecules is regarded as a nonisolated system. By using a self-consistency principle i.e., the identity of the autocorrelation function for all molecules, a fourth-order differential equation is derived, which in principle could be made to give a unique determination of the autocorrelation function. Two methods are given for finding an approximate solution. An alternative expression for the autocorrelation function is found by the introduction of ``collective'' coordinates. Comparison of this expression with the result obtained by the principle of self-consistency leads to a unique determination of the integral of the autocorrelation function. The result has a reasonable physical interpretation for the mechanism of correlation breakdown, namely, the transfer of energy from ``collective'' motion or sound waves to ``individual'' or ``average'' motion.