The compressibility theorem for quantum simple fluids at equilibrium

Abstract

An extension of the compressibility theorem for quantum simple fluids within the pathintegral approach is presented. First, it is demonstrated that in the absence of quantum exchange, the isothermal compressibility can be formulated in an exact manner with the use of the pair radial correlation function of the path-integral centroids corresponding to the particles of the fluid. This adds up to the two known formulations based on the pair correlations between true quantum particles, namely the instantaneous and the pair linear response correlations. To complement this extension, an exact Ornstein-Zernike equation for pair centroid correlations is derived, which permits accurate estimates for the isothermal compressibility to be obtained. Several fluids are studied, new numerical results for the latter quantity are reported to support the theoretical points, and some difficulties present in this sort of calculation are discussed. The systems studied are the following: the quantum hard sphere fluid with and without attractive Yukawa interaction, liquid helium-4 and liquid para-hydrogen. Finally, the possibilities of extending the theorem to deal with quantum exchange are considered, and it is shown that the extension and its computational Ornstein-Zernike scheme also hold for a Bose fluid.