COLLECTIVE MOTIONS IN LIQUIDS WITH A NORMAL-MODE APPROACH

We present a theory of collective dynamics in simple liquids within a harmonic approximation. We extend the normal mode approximation, which has previously been applied to single-particle properties, such as the velocity autocorrelation function, to the calculation of the longitudinal and transverse particle current autocorrelation functions. Within the harmonic approximation, these autocorrelation functions may be related to a configuration-averaged phonon Green's function, which is a generalization of the conventional Green's function for a perfect crystal. We show that the calculation of this Green's function is equivalent to the evaluation of a propagator in a random walk problem, in which a walker with internal states hops among sites located at the particles of the fluid. We develop an approximate, self-consistent theory for this Green's function, which is used to calculate the longitudinal current correlation function for a dense Lennard-Jones fluid. The results are compared to previous computer simulations of this correlation function.