An application of the self-consistent variational effective potential against the path-integral to compute equilibrium properties of quantum simple fluids

Abstract

The thermodynamic and structural features obtained from the self-consistent variational effective potential SCP (developed by Feynman and Kleinert and by Giachetti and Tognetti) in the study of quantum fluids are analysed, taking the full path-integral (PI) treatment as a reference and helium-4 as a probe. Within the SCP method the pair radial distribution functions are of two types: one describing the correlations between the centroids of the quantum particles, and the other describing the true correlations between quantum particles. An analytical derivation states that the SCP picture for quantum particles does not distinguish between the instantaneous and the linear response pair radial distribution functions, which otherwise can be defined within a full path-integral framework by considering equal imaginary time or mixed imaginary time averages, respectively. It is also shown how the centroid and true quantum particle pair radial distribution functions are connected through a convolution. Explicit formulae for both the isotropic effective potential (ISCP) and the more general ani-sotropic effective potential (ASCP) pair radial distribution functions are given, and the possibilities of computing SCP static structure factors are discussed. Monte Carlo simulations of dense fluid Lennard-Jones helium-4 have been performed with ISCP and PI (PIMC) to determine the proximity between both methods, and to avoid spurious singularities in ISCP, use of a fourth-order Taylor expansion is made (TISCP). Within the conventional Ornstein-Zernike framework two evaluations of the structure factor are carried out. Wherever possible results are compared with experiment and data reported in the literature, and reliable limits of applicability for TISCP are reported.