A diagrammatic kinetic theory of density fluctuations in simple liquids in the overdamped limit. II. The one-loop approximation

Abstract

A diagrammatic kinetic theory of density fluctuations in simple dense liquids at long times, described in Paper I, is applied to a high density Lennard-Jones liquid to calculate various equilibrium time correlation functions. The calculation starts from the general theory and makes two approximations. (1) The general diagrammatic expression for an irreducible memory kernel is approximated using a one-loop approximation. (2) The generalized Enskog projected propagator, which is required for the calculation, is approximated using a simple kinetic model for the hard sphere memory function. The coherent intermediate scattering function (CISF), the longitudinal current correlation function (LCCF), the transverse current correlation function (TCCF), the incoherent intermediate scattering function (IISF), and the incoherent longitudinal current correlation function are calculated and compared with simulation results for the Lennard-Jones liquid at high density. The approximate theoretical results are in good agreement with the simulation data for the IISF for all wave vectors studied and for the CISF and LCCF for large wave vector. The approximate results are in poor agreement with the simulation data for the CISF, LCCF, and TCCF for small wave vectors because these functions are strongly affected by hydrodynamic fluctuations at small wave vector that are not well described by the simple kinetic model used. The possible implications of this approach for the study of liquids are discussed.