Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Low-density expansions, computer experiments, and the ground-state energy of hard-sphere fluids

Valdir C. Aguilera-Navarro, Shirley Ho, MANUEL DE LLANO

Published Dec 1, 1987• 8 citations
Publisher

Abstract

A family of extrapolants somewhat more general than Pad\'e approximants is presented and applied to the low-density ground-state energy expansions which systematic quantum-field-theoretic infinite-partial-summation techniques have produced for many-boson and many-fermion systems of hard spheres. The existence of a quantum close-packing ultimate system density, as well as monotonic-increasing energy as function of density, is assumed in narrowing down the possible extrapolants appropriate for moderate to high densities. Of those remaining, excellent agreement is found at physical densities, and almost unique selections at higher densities, which are consistent both with available Green-function Monte Carlo data as well as with a feasible overall picture of ultimate-density pole placements.

DOI
10.1103/physreva.36.5742

Related papers

Improved quantum hard-sphere ground-state equations of state

M. A. Solís, MANUEL DE LLANO, J. W. Clark +1 more

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 regular (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are constructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, extrapolated to intermediate densities via Padé and other approximants, but whose ultimate density is irregular or 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.

arXiv:0705.1191•Physical Review E•Sep 20, 2007•2 citations

Hard-core square-well fermions

George Allen Baker Jr., L. P. Benofy, Mauricio Fortes +3 more

Based on the well-known low-density expansion for the ground-state energy per particle of a many-fermion system interacting pairwise via a central potential we develop a perturbation scheme in which the zero-order state is that of the purely-repulsive-spheres fluid. For the hard-core plus square-well pair-interaction case we have deduced, for two-species fermion matter, perturbation formulas up to sixth order in the attractive coupling parameter. We explicitly report results up to fourth order here. Pad\'e-approximant analyses in the density are carried out in each order with the intent of providing the basis necessary for extensive equation-of-state calculations of various many-fermion systems. In particular, for zero order (the fermion hard-sphere fluid) we predict an uncertainty-principle divergence in the energy, and hence pressure, corresponding to the random close packing of spheres, at a density of about 0.5 times the recently obtained value for boson hard spheres and about 0.2 times the well-known empirical value for classical hard spheres.

Physical Review A•Dec 1, 1982•30 citations

Thermodynamic perturbation theory of hard-core square-well bosons

C Keller, Valdir C. Aguilera-Navarro, MANUEL DE LLANO

The authors investigate the calculational scheme for an eventual first-principles description of the ground-state energy of the many-boson Schrodinger equation. They employ a model 4 He intermolecular pair potential consisting of a hard core surrounded by an attractive rectangular well. The study is based on the well known low-density expansion for such a system, where three coefficients are known. The first corrections to the fourth coefficient are determined on the basis of the rearranged series being a thermodynamic perturbation expansion, namely one representing perturbation not about the ideal gas but about the hard-sphere fluid. Pade approximants, and variations thereof, are employed to extrapolate to physical regimes in both resulting series, in density as well as in the attractive coupling constant.

Journal of Physics A Mathematical and General•Feb 7, 1988•3 citations

Ground state energy of a hard-sphere Fermi fluid

George Allen Baker Jr., L. P. Benofy, Mauricio Fortes +1 more

A new method of computing the ground state energy of a Fermi fluid is developed and applied to the hard-sphere Fermi fluids of two and four components. We find the results to be highly accurate for low densities. In this paper we compute and report the perturbation series for the ground state energy for the soft, repulsive, square-well problem at a number of densities for a four-component Fermi system as well as the ladder approximation energies for a hard-sphere potential at the same densities.

Physical Review C•Aug 1, 1986•7 citations

Ground-state Lennard-Jones and Aziz boson liquids: Perturbation theory and computer experiment

Christina Keller, MANUEL DE LLANO, Siheng Ren +2 more

The exact, low-density many-boson expansion for the ground-state energy is rearranged in a quantum-thermodynamic perturbation series. Extrapolation to physical densities is implemented order by order via Pad\'e-type approximants. Several ways of splitting the pair Lennard-Jones (LJ) or Aziz potentials are considered, including the Barker-Henderson (BH) and Weeks-Chandler-Andersen (WCA) schemes familiar from classical fluid studies. Results obtained using the LJ interaction with WCA splitting, when compared with benchmark simulation data, agree excellently in energy and density, but only moderately so in sound velocity. For the Aziz potential, however---perhaps because of a softer core and/or its ability to support a two-particle bound state---, neither potential splitting (BH or WCA) gave results of the LJ quality, but a method intermediate between BH and WCA proves to be superior. Our results are also compared with other recent alternative calculations, both variational and perturbative.

Physical review. B, Condensed matter•Dec 1, 1989•8 citations

Application of parquet perturbation theory to ground states of boson systems

Andrew David Jackson, Alexander Lande, R. W. Guitink +1 more

In the interest of polishing the parquet approach to microscopic calculations of ground-state properties of zero-temperature quantum fluids, we have developed a perturbative scheme for the systematic improvement of the four-point function which retains the correct behavior of the parquet diagrams in both the small-r and small-k limits. Numerical implementation of this scheme indicates significantly improved agreement with binding energies calculated with Green's-function Monte Carlo techniques (i.e., differences in liquid $^{4}\mathrm{He}$ are less than 1.5%). The charged Bose gas and the hard-sphere system are also considered. Remaining difficulties in the calculations of the liquid structure function are noted and discussed.

Physical review. B, Condensed matter•Jan 1, 1985•27 citations
A family of extrapolants somewhat more general than Pad'e approximants is presented and applied to the low-density ground-state energy expansions which systematic quantum-field-theoretic infinite-partial-summation techniques have produced for many-boson and many-fermion systems of hard spheres. The existence of a quantum close-packing ultimate system density, as well as monotonic-increasing energy as function of density, is assumed in narrowing down the possible extrapolants appropriate for moderate to high densities. Of those remaining, excellent agreement is found at physical densities, and almost unique selections at higher densities, which are consistent both with available Green-function Monte Carlo data as well as with a feasible overall picture of ultimate-density pole placements.
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 regular (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are constructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, extrapolated to intermediate densities via Padé and other approximants, but whose ultimate density is irregular or 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.
Based on the well-known low-density expansion for the ground-state energy per particle of a many-fermion system interacting pairwise via a central potential we develop a perturbation scheme in which the zero-order state is that of the purely-repulsive-spheres fluid. For the hard-core plus square-well pair-interaction case we have deduced, for two-species fermion matter, perturbation formulas up to sixth order in the attractive coupling parameter. We explicitly report results up to fourth order here. Pad\'e-approximant analyses in the density are carried out in each order with the intent of providing the basis necessary for extensive equation-of-state calculations of various many-fermion systems. In particular, for zero order (the fermion hard-sphere fluid) we predict an uncertainty-principle divergence in the energy, and hence pressure, corresponding to the random close packing of spheres, at a density of about 0.5 times the recently obtained value for boson hard spheres and about 0.2 times the well-known empirical value for classical hard spheres.
The authors investigate the calculational scheme for an eventual first-principles description of the ground-state energy of the many-boson Schrodinger equation. They employ a model 4 He intermolecular pair potential consisting of a hard core surrounded by an attractive rectangular well. The study is based on the well known low-density expansion for such a system, where three coefficients are known. The first corrections to the fourth coefficient are determined on the basis of the rearranged series being a thermodynamic perturbation expansion, namely one representing perturbation not about the ideal gas but about the hard-sphere fluid. Pade approximants, and variations thereof, are employed to extrapolate to physical regimes in both resulting series, in density as well as in the attractive coupling constant.
The exact, low-density many-boson expansion for the ground-state energy is rearranged in a quantum-thermodynamic perturbation series. Extrapolation to physical densities is implemented order by order via Pad\'e-type approximants. Several ways of splitting the pair Lennard-Jones (LJ) or Aziz potentials are considered, including the Barker-Henderson (BH) and Weeks-Chandler-Andersen (WCA) schemes familiar from classical fluid studies. Results obtained using the LJ interaction with WCA splitting, when compared with benchmark simulation data, agree excellently in energy and density, but only moderately so in sound velocity. For the Aziz potential, however---perhaps because of a softer core and/or its ability to support a two-particle bound state---, neither potential splitting (BH or WCA) gave results of the LJ quality, but a method intermediate between BH and WCA proves to be superior. Our results are also compared with other recent alternative calculations, both variational and perturbative.
In the interest of polishing the parquet approach to microscopic calculations of ground-state properties of zero-temperature quantum fluids, we have developed a perturbative scheme for the systematic improvement of the four-point function which retains the correct behavior of the parquet diagrams in both the small-r and small-k limits. Numerical implementation of this scheme indicates significantly improved agreement with binding energies calculated with Green's-function Monte Carlo techniques (i.e., differences in liquid 4He^{4}\mathrm{He}4He are less than 1.5%). The charged Bose gas and the hard-sphere system are also considered. Remaining difficulties in the calculations of the liquid structure function are noted and discussed.