Improved Quantum Hard-Sphere Ground-State Equations of State

TL;DR

This paper presents improved equations of state for quantum hard-sphere systems, incorporating corrections and extrapolations that align well with advanced simulation data for both bosons and fermions.

Contribution

It introduces corrected and generalized ground-state energy formulas for boson and fermion hard-sphere systems, improving agreement with simulation results.

Findings

Enhanced agreement with Monte Carlo simulation data.

Refined equations of state for bosons and fermions.

Identification of irregular close-packing densities.

Abstract

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a sphere-of-influence picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate \textit{regular} (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are contructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, appropriately extrapolated to intermediate densities, but whose ultimate density is irregular or \textit{random} closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L-expansion data for two-component fermions.