Virial expansions for quantum plasmas: Fermi-Bose statistics

This paper is devoted to the calculation of the density expansions (at fixed non-zero temperature) of the thermodynamic functions for quantum plasmas. The Maxwell-Boltzmann forms of these expansions have been studied in two previous papers. Here we include the exchange contributions due to Fermi or Bose statistics, via a perturbative scheme where the reference ingredients are computed in the framework of Maxwell-Boltzmann statistics. The whole scheme is based on the Feynman-Kac path integral representation which amounts to introducing classical auxiliary systems made of extended objects, the filaments. The quantities of interest are then evaluated by applying familiar diagrammatical methods of classical statistical mechanics. The exact density expansions of the free energy and of the pressure are explicitly calculated up to order rho(5/2) in the density rho. The corresponding expressions include, in a systematic and coherent way, the contributions of various physical effects such as screening, diffraction, recombination, scattering, and exchange. At order rho(2), we recover the expansions obtained via the effective-potential method. Our terms of order rho(5/2) correctly reproduce results which are known in some particular limits. Moreover, the high-temperature expansions which can be easily inferred from our virial expansions do coincide with those obtained from the Feynman graphs in the usual many-body theory.