The general expression for the transport coefficients at finite frequency is given by the spectral function of the autocorrelation of the flux corresponding to the transport phenomenon considered. Because the explicit analytical solution of such a correlation function involves the whole many-body problem for strongly coupled systems, appeal must be made to a model in order to derive the explicit frequency dependence of the transport functions. In the first part of this paper, we calculate these functions analytically [i.e., the diffusion $D\left(\omega \right)$, the viscosities ${\eta }_S\left(\omega \right)$ and ${\eta }_B\left(\omega \right)$, and the thermal conducti̧vity $\kappa \left(\omega \right)$] from the generalized Berne-Boon-Rice model. The frequency dependence of these transport functions becomes significant at high frequencies, i.e., when $\omega$ approaches ${\omega }_c\sim {\tau }_c^{-1\mathrm{}}$, where ${\tau }_c$ is the collision time, and should be essentially responsible for the departure from classical hydrodynamics. This is shown in Sec. II of this paper, where we present a calculation of the spectral distribution of the light scattered from thermal fluctuations in simple fluids. When the transport functions are introduced in the hydrodynamic equations to replace the usual constant transport coefficients, the spectrum of the scattered light is modified significantly, to second order in $\Gamma k^2$, where $\Gamma$ is essentially a linear function of the transport functions. The second-order spectrum obtained here is in agreement with previous results, but it is shown that the main effect arises from the frequency dependence of the transport functions, which was ignored in previous work. These effects induce a small but significant negative dispersion in the first-sound velocity. This prediction is in qualitative agreement with the recent light scattering experiments by Fleury and Boon on liquid argon, which were initially interpreted as a possible experimental observation of the frequency dependence of the transport functions in simple liquids.

• Received 1 May 1970

DOI:https://doi.org/10.1103/PhysRevA.2.2542