Sum rules and atomic correlations in classical liquids

Abstract

The sixth frequency moment of the spectral functions of both the longitudinal and transverse current correlations along with their self-parts has been derived for a system of particles interacting through a two-body potential. The first two frequency moments of the spectral function of the energy-density fluctuation, and the first four frequency moments of the spectral function of the kinetic-energy-density fluctuation-correlation functions have also been derived. Numerical estimates for the fourth and sixth frequency moments of the spectral function of the longitudinal current correlations have been made for liquid argon. From this some information about the behavior of the contributions of triplet and quadruplet correlation functions to the frequency moments of liquid argon have been obtained. Numerical estimates have also been made for the first four frequency moments of the kinetic-energy-density fluctuation-correlation function in the long-wavelength limit for liquid argon.