• Corpus ID: 249890046

Energy functionals of single-particle densities: A unified view

@inproceedings{Englert2022EnergyFO,
  title={Energy functionals of single-particle densities: A unified view},
  author={Berthold-Georg Englert and Jun Hao Hue and Zichang Huang and Mikolaj M. Paraniak and Martin Trappe},
  year={2022}
}
Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a second-quantized perspective and introduce a version of density functional theory that treats all single-particle contributions to the energy exactly. An appendix deals with semiclassical eigenvalues. 

References

SHOWING 1-10 OF 49 REFERENCES
Semiclassical quantization in momentum space.
  • Rohwedder, Englert
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1994
Three-dimensional, spherically symmetric Hamilton operators, which consist of the sum of an arbitrary effective kinetic energy and an attractive Coulomb potential, are quantized semiclassically. The
Perspective on “Density-functional theory for fractional particle number: derivative discontinuities of the energy”
Abstract. This paper provides an overview of the title paper by Perdew, Parr, Levy and Balduz [Phys Rev Lett 49:1691 (1982)]. The title paper extended density functional theory to fractional electron
Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction
In order to calculate the average value of a physical quantity containing also many-particle interactions in a system of $N$ antisymmetric particles, a set of generalized density matrices are
Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory
TLDR
Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers, underscore the importance of grand canonical ensemble formulation in density functional theory.
Density functional of a two-dimensional gas of dipolar atoms: Thomas-Fermi-Dirac treatment
We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac
Density-potential functional theory for fermions in one dimension
We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg–Kohn density functional theory. DPFT resolves the usual trouble with the
Energy functionals in momentum space: Exchange energy, quantum corrections, and the Kohn-Sham scheme.
  • Cinal, Englert
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1993
TLDR
The energy functionals thus refined are used to introduce a Kohn-Sham scheme for self-consistent momentum-space calculations to helium and beryllium, and the total binding energies predicted are somewhat better than those of the configuration-space method.
Statistical theory of the atom in momentum space
In 1992, Englert [Phys. Rev. A, 45;127--134] found a momentum energy functional for atoms and discussed the relation to the Thomas-Fermi functional (Lenz [Z. Phys., 77;713--721]). We place this model
Semiclassical theory of trapped fermionic dipoles
We investigate the properties of a degenerate dilute gas of neutral fermionic particles in a harmonic trap that interact via dipole-dipole forces. We employ the semiclassical Thomas-Fermi method and
Semiclassics: The hidden theory behind the success of DFT
It is argued that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total
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