Collective and Single-Particle Effects in Autocorrelation Functions for Dense Classical Fluids

Approximate equations of motion for the single-particle autocorrelation function $f(\overrightarrow{\mathrm{k}},\overrightarrow{\mathrm{p}},{\overrightarrow{\mathrm{p}}}^{\prime },t)$ in a classical fluid are considered. The interaction term is treated by expanding it in powers of the approximate collective coordinates of the system. In the detailed calculations, only terms linear in the collective coordinates are retained. Two models are considered using two sets of variational collective modes. If the isothermal sound mode introduced by Zwanzig is used, a more physically transparent derivation of the modified linear Vlasov equation, obtained earlier by several authors, results. The phononlike modes introduced by Nossal and Zwanzig give a new and significantly improved result which leads directly to closed expressions for the longitudinal and transverse current-current correlation functions. The models presented show a clear separation of structural, dynamic, and thermal motion effects when analyzed in terms of appropriately defined memory functions. Extensions of the model results which replace free-particle motion by the "self-motion" of an atom in the fluid are naturally suggested, though no satisfactory theoretical justification for these extensions is given. The extension of the modified linear Vlasov equation is the same as proposed earlier by Kerr. The extension of our phononlike model is a new result which is expected to give improved agreement with experiment.