Thermodynamic and structural properties of the path-integral quantum hard-sphere fluid

Abstract

An extensive study of the path-integral quantum hard-sphere fluid far from exchange is presented. The results cover the calculation of mechanical, thermal, r-space and k-space pair properties. Path-integral Monte Carlo simulations involving the Cao–Berne’s propagator provide the internal energies and pair radial distribution functions (instantaneous, linear response, and necklace center of mass). For the sake of comparison, Barker’s and Jaccuci–Omerti’s image propagators are also applied at several state points. To obtain k-space properties use of the Gaussian Feynman–Hibbs picture for representing quantum systems is made. This picture is known to yield two Ornstein–Zernike equations; one for true quantum particles (linear response) and the other for the centers of mass of quantum particles. Direct correlation functions and static structure factors are obtained via Baxter’s partition complemented with Dixon–Hutchinson’s variational procedure. Wherever possible, the present results are compared with semiclassical (Yoon–Scheraga’s) and path-integral (Runge–Chester’s) data available in the literature. The limits of validity of the Gaussian Feynman–Hibbs picture in this context are also established.