Generalized Hydrodynamics and Time Correlation Functions

Abstract

Time correlation functions in classical liquids at high frequencies (${10}^{12}$ ${\sec }^{-1\mathrm{}}$) and short wavelengths (${10}^{-8\mathrm{}}$ cm) are analyzed using linear response theory of Martin and Kadanoff. Rigorous expressions, based on dispersion relation, sum rules, and limiting behavior at long wavelengths and low frequencies, are obtained in terms of damping (or memory) function. Specific assumptions regarding the damping function then enable numerical results to be obtained which are compared with computer molecular-dynamics experiments and inelastic neutron-scattering on liquid argon. It is shown that all the known characteristic features of density and current correlations are reproduced using a Lorentzian frequency dependence of the damping function. In particular, the frequency wave-number relation for excitations described by the longitudinal current correlation is in quantitative agreement with the computer calculations. Relaxation times are derived from the computer results on transverse and longitudinal current correlations, and the van Hove self-(test-particle) correlation. These times exhibit significant variation with wavelength, and all have magnitudes of approximately 1 × ${10}^{-13\mathrm{}}$ sec. Present analysis is also applicable to slow neutron-scattering experiments. Coherent- and incoherent-scattering contributions in argon are computed without any adjustable parameter, and the theoretical absolute-scattering intensities are in quite good agreement with experimental data.