Kinetic theory of density fluctuations in a one-component monatomic fluid at equilibrium: A short time theory for the memory function

A diagrammatic formulation of kinetic theory of fluctuations in equilibrium classical fluids is used to investigate the short time behaviour of the memory function for density fluctuations. We consider a model system, such as the Lennard-Jones potential, that contains both strongly repulsive forces and weaker attractive forces. We define a small parameter that is a measure of the, softness of the repulsive forces. The diagrams in the series for the memory function that are of lowest order in this small parameter for small times are identified and summed to get an expression for what we call the “short time approximation” (STA) for the memory function. The correlation function calculated using the STA describes the dynamics of the system as governed by a series of uncorrelated repulsive binary collisions.; We evaluate the matrix elements of the memory function in the short time approximation by performing two-particle trajectory calculations. We use these matrix elements in the differential equations and solve for the time correlation functions. The results are compared to computer simulation data for a Lennard-Jones fluid. We calculate the correlation functions at a high density near the triple point density and at temperatures from the triple point temperature to just above the critical temperature. The correlation functions that we calculate are scattering functions, current correlation functions and the velocity autocorrelation function. We also calculate self-diffusion coefficients and the viscosity coefficients using the long time behavior of the correlation functions.; The STA results are closer to the simulation results at high temperatures than at low temperatures, and at large wave vectors than at low wave vectors. The STA results are more accurate for self properties than for total properties. The self-diffusion coefficients and the viscosity coefficients can be understood on the basis of an Enskog theory for transport coefficients, modified for the case of continuous repulsive potentials with attractions.; Understanding the predictions of the short time approximation to the memory function will be useful in the development of a comprehensive kinetic theory of dense fluids that will work for all times.