Energy, Specific Heat, and Magnetic Properties of the Low-Density Electron Gas

Carr, W. J.

doi:10.1103/physrev.122.1437

Cited by 343 publications

(112 citation statements)

References 11 publications

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“…(12) very well, giving f 1 = 1.3379 and f 2 = −0.55270. These values are in reasonable agreement with the parameters found using a completely different method by Carr 20 and Carr, Coldwell-Horsfall and Fein 21 , who have calculated the zero-point lattice-vibrational energy of a Wigner crystal in order to give an analytical result of f 1 = 1.325. Furthermore, they use perturbation theory to obtain the approximate result f 2 = −0.365.…”

Section: Locating the Fluid-to-crystal Transition Densitysupporting

confidence: 76%

“…This can be understood in terms of Eq. (20). The potential energies of the fixed and floating crystals are the same, but their charge densities and PCFs are quite different.…”

Section: B Discussion and Results For The Pcfsmentioning

confidence: 85%

“…20 The first of these is taken to be f 0 = −0.89593 in order to give the Madelung energy in the low density limit. We found that our DMC data fitted Eq.…”

Section: Locating the Fluid-to-crystal Transition Densitymentioning

confidence: 99%

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Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

et al. 2004

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We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs = 100 to 150. We have tested different types of orbital for use in the approximate wave functions but none improve upon the simple Gaussian form. The Gaussian exponents are optimized by directly minimizing the diffusion quantum Monte Carlo energy. We have carefully investigated and sought to minimize the potential biases in our Monte Carlo results. We conclude that the uniform electron gas undergoes a transition from a ferromagnetic fluid to a body-centered cubic Wigner crystal at rs = 106±1. The diffusion quantum Monte Carlo results are compared with those from Hartree-Fock and Hartree theory in order to understand the role played by exchange and correlation in Wigner crystals. We also study "floating" Wigner crystals and give results for their pair correlation functions.

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Section: Locating the Fluid-to-crystal Transition Densitysupporting

confidence: 76%

“…This can be understood in terms of Eq. (20). The potential energies of the fixed and floating crystals are the same, but their charge densities and PCFs are quite different.…”

Section: B Discussion and Results For The Pcfsmentioning

confidence: 85%

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Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

et al. 2004

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“…In the harmonic approximation for the Coulomb crystal, Θ D ≈ 0.45 T p (Carr 1961). The Coulomb plasmas are called strongly coupled if the parameter Γ C = (Ze) 2 /a i T , which estimates the electrostatic to thermal energy ratio, is large.…”

Section: Basic Plasma Parametersmentioning

confidence: 99%

Neutron Stars—Cooling and Transport

2015

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Observations of thermal radiation from neutron stars can potentially provide information about the states of supranuclear matter in the interiors of these stars with the aid of the theory of neutron-star thermal evolution. We review the basics of this theory for isolated neutron stars with strong magnetic fields, including most relevant thermodynamic and kinetic properties in the stellar core, crust, and blanketing envelopes.

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“…67 The next term, +2.65/r 3/2 s ryd, describes the coupled harmonic zerotemperature motion in lowest order . 68,69,70 To estimate the corresponding n(k, r s ), we define with 3 ω/2 = 2.65/r …”

Section: Appendix B: the Momentum Distribution Of The Wigner Crystalmentioning

confidence: 99%

Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion

2002

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The momentum distribution of the unpolarized uniform electron gas in its Fermi-liquid regime, n(k, rs), with the momenta k measured in units of the Fermi wave number kF and with the density parameter rs, is constructed with the help of the convex Kulik function G(x). It is assumed that n(0, rs), n(1 ± , rs), the on-top pair density g(0, rs) and the kinetic energy t(rs) are known (respectively, from accurate calculations for rs = 1, ..., 5, from the solution of the Overhauser model, and from Quantum Monte Carlo calculations via the virial theorem). Information from the high-and the low-density limit, corresponding to the random-phase approximation and to the Wigner crystal limit, is used. The result is an accurate parametrization of n(k, rs), which fulfills most of the known exact constraints. It is in agreement with the effective-potential calculations of Takada and Yasuhara [Phys. Rev. B 44, 7879 (1991)], is compatible with Quantum Monte Carlo data, and is valid in the density range rs 12. The corresponding cumulant expansions of the pair density and of the static structure factor are discussed, and some exact limits are derived.

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Energy, Specific Heat, and Magnetic Properties of the Low-Density Electron Gas

Cited by 343 publications

References 11 publications

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

Neutron Stars—Cooling and Transport

Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion

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