Longitudinal modes, transverse modes and velocity correlations in liquids. I

Abstract

By constructing a microscopic form for the velocity field the author's have derived an expression for the velocity autocorrelation function in a simple liquid. It represents an analysis of the correlation function in terms of the longitudinal and transverse momentum current densities and correctly describes both the long and short time behaviour. The authors have applied the result to a model of liquid rubidium in order to see how the collective modes in the system influence the individual particle motion. It is found that the longitudinal current component is responsible for the oscillatory behaviour of the velocity autocorrelation function; the principle peak in the associated frequency spectrum is generated by the coupling of the particle velocity to the transverse current; the coupling to the longitudinal current produces the peak or shoulder at higher frequencies which is observed in computer experiments; and the diffusion coefficient is determined almost entirely by the transverse current component.