Dynamical pair correlations of classical and quantum fluids perturbed with weak long-range forces

We study time dependent correlation functions of ideal classical and quantum gases using methods of equilibrium statistical mechanics. The basis for this is the path integral formalism of quantum mechanical systems. By this approach the statistical mechanics of a quantum mechanical system becomes the equivalent of a classical polymer problem in four dimensions where imaginary time is the fourth dimension. Several non-trivial results for quantum systems have been obtained earlier by this analogy. Here we will focus upon particle dynamics. First ideal gases are considered. Then interactions, that are assumed weak and of long range, are added, and methods of classical statistical mechanics are applied to obtain the leading contribution. Comparison is performed with known results of kinetic theory. These results demonstrate how methods developed for systems in thermal equilibrium also is applicable outside equilibrium. Thus, more generally, we have reason to expect that these methods will be accurate and useful for other situations of interacting many-body systems consisting of quantized particles too. To indicate so we sketch the computation of the induced Casimir force between parallel plates filled with ions for the situation where the ions are quantized, but the interaction remains electrostatic. Further in this respect we establish expressions for a leading correction to ab initio calculations for the energies of the quantized electrons of molecules. To our knowledge these two latter applications go beyond earlier results.