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 th e velocity autocorrelation function, to the calculation of the longitu dinal and transverse particle current autocorrelation functions. Withi n the harmonic approximation, these autocorrelation functions may be r elated to a configuration-averaged phonon Green's function, which is a generalization of the conventional Green's function for a perfect cry stal. We show that the calculation of this Green's function is equival ent to the evaluation of a propagator in a random walk problem, in whi ch a walker with internal states hops among sites located at the parti cles of the fluid. We develop an approximate, self-consistent theory f or this Green's function, which is used to calculate the longitudinal current correlation function for a dense Lennard-Jones fluid. The resu lts are compared to previous computer simulations of this correlation function.