Quantum-Hard-Sphere System Equations of State Revisited

Keller, Christina; Llano, M. de; Ren, Shisong; Solís, M. A.; Baker, George A.

doi:10.1006/aphy.1996.0107

Cited by 4 publications

(18 citation statements)

References 20 publications

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“…Improvements with respect to previous work (notably but not exclusively that of Ref. [24]) have been achieved by assuming i) that the classical random closest close-packing hard-sphere densities are the ultimate fluid densities at which the energy diverges with a second-order pole and ii) proposing and imposing a value for the residue at the pole that is the same for either bosons or fermions as closest close-packing is approached and the hard spheres become distinguisable. Implementing these two conditions and taking advantage of recent diffusion Monte Carlo simulation data has allowed us to incorporate an additional term in the low-density expansion beyond that employed in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…Implementing these two conditions and taking advantage of recent diffusion Monte Carlo simulation data has allowed us to incorporate an additional term in the low-density expansion beyond that employed in Ref. [24]. The resulting determination of the best approximants has produced decidedly improved results for bosons as well as for two-component fermions, but not for four-component fermions.…”

Section: Discussionmentioning

confidence: 99%

“…However, this function does not have a zero in the region of physical interest, i.e., 0 ≤ ρ/ρ 0 ≤ 1, which implies 0 ≤ x ≡ k F c ≤ 3.47 since ρ = k sphere system: XI is the fluid branch approximant of Ref. [24], Fig. 2; B2 refers to (22) and (24) with A ≃ 11.9; ML is the modified London formula (1).…”

Section: Fermions With ν =mentioning

confidence: 99%

“…7 we compare both the new improved expression [3/3](x) and the previous best energy expression, i.e, the two-point Padé approximant [3//2](x) reported in Ref. [24] and supported by Ladder, VFHNC and L-expansion data. Table 3: The F 5 and F 6 coefficients for ν = 2 that follow from conditions (38) and (39) …”

Section: Fermions With ν =mentioning

confidence: 99%

“…However, one can extrapolate the series for hard-sphere systems to physical and even to close-packing densities through the use of Padé [20] and/or a modest extension of these called the "tailing" [21] approximants. The so-called quantum thermodynamic (or van der Waals) perturbation theory (QTPT) [22,23] has provided fairly accurate representations of the fluid branch of the equation of state of quantum hard-sphere systems [24], even beyond freezing (or, Kirkwood) phase transition densities, but without sufficient credibility as one approaches close packing. This is clear since one does not possess a single ground-state energy function with implicit information of both fluid and crystalline branches, with presumably different close-packing ultimate densities.…”

Section: Introductionmentioning

confidence: 99%

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Improved quantum hard-sphere ground-state equations of state

et al. 2007

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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 hardsphere 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 contructed 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.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Fermions With ν =mentioning

confidence: 99%

Section: Fermions With ν =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved quantum hard-sphere ground-state equations of state

et al. 2007

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Extrapolation of perturbation-theory expansions by self-similar approximants

Gluzman¹,

Yukalov²

2014

Eur. J. Appl. Math

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The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures.

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Equation of state for a partially ionized gas

Baker

1997

Phys. Rev. E

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The derivation of equations of state for fluid phases of a partially ionized gas or plasma is addressed from a fundamental point of view. First, a cubic cellular model and then a spherical cellular model is deduced for the hot curve limit ͑or ideal Fermi gas͒. Next the Coulomb interactions are added to the spherical model for general ionic charge Z. A numerical example of the theory for the case of hydrogen is reported, and it reduces in various limits of temperature and density to the expected behavior. It displays an electron, localizationdelocalization phase transition of the normal liquid-gas character.

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Quantum-Hard-Sphere System Equations of State Revisited

Cited by 4 publications

References 20 publications

Improved quantum hard-sphere ground-state equations of state

Improved quantum hard-sphere ground-state equations of state

Extrapolation of perturbation-theory expansions by self-similar approximants

Equation of state for a partially ionized gas

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