Density Fluctuations in Single-Component Fluids

The memory-function formalism of Zwanzig and Mori is used to study the density-density correlation function $〈\tilde{\rho }\mathrm{}\left(S\right)\mathrm{}{\rho }^{*}〉$ in a single-component fluid. Using the hydrodynamic variables suitable for longitudinal disturbances, $〈\tilde{\rho }\mathrm{}\left(S\right)\mathrm{}{\rho }^{*}〉$ is expressed in terms of the appropriate memory functions. This formally exact relation is then shown to be equivalent to the result obtained by Kadanoff and Martin in terms of a dispersion function. By considering the approximations suitable for the analysis of Brillouin scattering experiments, it is also shown that the formal expression for $〈\tilde{\rho }\mathrm{}\left(S\right)\mathrm{}{\rho }^{*}〉$ can be reduced to results previously derived by Mountain and by Bhatia and Tong on the basis of a macroscopic analysis using the linearized hydrodynamic equations coupled either with relaxing shear and bulk viscosities or with thermodynamic relaxation theory. Present analysis thereby provides a microscopic basis for these hydrodynamic theories, as well as revealing to some extent the nature of approximations involved. Our microscopic analysis also suggests a simple model to take into account the effects of coupling between heat flux and the viscosity stress tensor.