Renormalized Kinetic Theory of Dense Fluids

Abstract

The purpose of this review, which belongs to the series on time-depen­ dent statistical mechanics (1-4), is to assess the current status of kinetic theory description of thermal fluctuations in a dense fluid. The quanti­ ties of interest are the space-time correlation functions through which one can study theoretically and experimentally the nonequilibrium properties of many-body systems. Besides the review articles in these volumes, there exist recent reviews (5, 6) and monographs (7-9) dealing with the methods for calculating time correlation functions and the study of dynamics of simple liquids. Reviews (10-12) and a monograph (13) on the kinetic theory approach have also appeared. In the present discussions we focus on fluctuations at finite wavelengths and frequen­ cies and emphasize the direct confrontation between theoretical predic­ tions and experimental data. The problem to be addressed is the derivation of a kinetic equation for fluids over a wide range of density and without restrictions on the range of space-time variations, and the demonstration of the validity of such an equation. For dilute fluids the appropriate kinetic equation is the well-known linearized Boltzmann equation or its generalization to arbitrary frequency and wavelength. These equations involve only un­ correlated binary collisions, and they are computationally tractable. For dense fluids an appropriate equation that treats the dynamics realisti­ cally and is yet tractable for practical calculations is still a subject of active investigation. The development and analysis of equations of this kind is therefore the central theme of our review. There exists a reasonable amount of experimental results to indicate what are the important effects to consider in developing a kinetic theory description of dense fluids. These effects are not unique to kinetic