A kinetic theory of classical simple liquids

Abstract

A dynamical equation for simple classical liquids is presented which is obtained by a systematic approximation for the memory function of the conventional, equilibrium-averaged, phase-space correlation function. This "kinetic" equation is non-Markovian and spatially nonlocal. It agrees with the known limiting behavior at high and low frequencies $\ensuremath{\omega}$ and wave vectors $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ even for dense liquids. For intermediate $k$ and $\ensuremath{\omega}$, our equation represents an explicit interpolation model from which virtually all measurable dynamical properties of the simple one-component fluid can be obtained. This equation can be solved analytically. As an example, the dynamical structure factor ${S}_{\mathrm{nn}}(k, \ensuremath{\omega})$ for liquid argon near its triple point was calculated. Our results are in excellent agreement with both coherent-neutron-scattering experiments (for $k=1\ensuremath{-}4$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$) and computer-dynamics results (for $k<1$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$). We want to emphasize that no adjustable parameters are introduced. We believe that this is the first kinetic theory which gives satisfactory results for ${S}_{\mathrm{nn}}(k, \ensuremath{\omega})$ for the full range $k$, $\ensuremath{\omega}$ for which data are available.