Fluctuation Analysis in Simple Fluids

Abstract

A classical analysis of time correlations in simple fluids based on the generalized Langevin equation is presented. Formulas for the current-current correlations are developed explicitly in a region of frequencies ($\ensuremath{\omega}\ensuremath{\sim}{10}^{13}$ ${\mathrm{sec}}^{\ensuremath{-}1}$) and wave numbers ($k\ensuremath{\sim}{10}^{8}$ ${\mathrm{cm}}^{\ensuremath{-}1}$) which are explored in typical slow-neutron-scattering measurements. Where applicable, comparisons are made with the results of the numerical calculations of Rahman in argonlike liquids, and good agreement is generally found. The analysis is based on a hydrodynamic description of fluids involving frequency- and wavelength-dependent transport parameters. The frequency and wavelength dependence of shear and longitudinal viscosities are given explicitly for argon-like liquids.