A Diagrammatic Formulation of the Kinetic Theory of Fluctuations in Equilibrium Classical Fluids. II. Equations of Motion of the Fluctuation Fields and Their Diagrammatic Solution

摘要

This is the second of a series of papers that presents a kinetic theory of fluctuations in equilibrium classical fluids that (i) makes extensive use of diagrammatic techniques in its development and (ii) will facilitate the use of diagrammatic techniques in the derivation of approximate kinetic theories. We focus on atomic liquids, but the results are easily generalizable to molecular liquids. The fundamental fluctuating quantity in the theory is f(R,P), which is the density of atoms at points in single particle phase space. The time correlation function for fluctuations of this quantity from its average, <δf(R,P,t)δ(R',P't')>, is the most basic correlation function of concern in generalized kinetic theories of fluctuations in liquids. In this paper, we derive a diagrammatic expression for this correlation function and for multipoint generalizations of it. The result allows us to make contact with the fully renormalized kinetic theory of Mazenko and show the equivalence of the results of the current approach to those of Mazenko; it is also the starting point for a graphical analysis of the various multipoint functions that appear in the renormalized kinetic theory.