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

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

The euler equation for the BDJ correlation function of a many-fermion system when a closed-form energy expression is used

Eirene Mavrommatis

Published Apr 1, 1977• 1 citation
Publisher
DOI
10.1007/bf02730013

Related papers

The modified Euler equation for the correlation function in the case of a many-fermion system and study of its asymptotic behaviour

M. E. Grypeos, Eirene Mavrommatis

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento•Sep 1, 1974•5 citations

Modified euler equations for the correlation function in the case of impure nuclear matter and other many-particle systems

M. E. Grypeos

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento•Mar 1, 1974•5 citations

Method of correlated basis functions for the ground state of a one-dimensional many-particle boson system

Deok Kyo Lee, Lin-ing Kung

The method of correlated basis functions is used in the study of the ground-state properties of a one-dimensional system of bosons interacting through a repulsive $\ensuremath{\delta}$-function potential. Ground-state energies are determined numerically for intermediate values of the coupling constant in three steps: (1) a trial form of the radial distribution function generated by the Bijl-Dingle-Jastrow (BDJ) type of wave function is introduced to obtain approximate ground-state energies, (2) the paired-phonon analysis is applied to improve the BDJ description of the ground state, and (3) leading corrections to the improved approximate energies are evaluted from the second-order perturbation energy generated by the three-phonon vertex. The obtained energy values are found to agree closely with the exact results calculated by Lieb and Liniger.

Physical review. B, Solid state•Jul 1, 1975•2 citations

Complete functional theory for the fermion density of independent particles subject to harmonic confinement in d dimensions for an arbitrary number of closed shells

I. A. Howard, N. H. March, Luis Miguel Nieto

In earlier work, expressions have been constructed for the single-particle kinetic-energy functional ${T}_{s}[\ensuremath{\rho}]$ for independent fermions subject to harmonic confinement in low dimensions, with $\ensuremath{\rho}$ the particle density. Here, the differential equation for $\ensuremath{\rho}$ is first obtained in d dimensions for an arbitrary number of closed shells. Then, by using the known Euler-Lagrange equation, the functional derivative $\ensuremath{\delta}{T}_{s}/\ensuremath{\delta}\ensuremath{\rho}(\mathbf{r})$ is constructed. ${T}_{s}[\ensuremath{\rho}]$ itself is proved to take the form of a linear combination of three pieces: (i) a von Weizs\"acker inhomogeneity kinetic energy, but with the original coefficient reduced by a dimensionality factor $1/d,$ (ii) a Thomas-Fermi kinetic energy, and (iii) a truly nonlocal contribution that, however, is shown to involve only the density $\ensuremath{\rho}$ itself and its first derivative. Thus, for this model, which is currently highly relevant to the interpretation of experiments on the evaporative cooling of dilute, and hence almost noninteracting, fermions, a complete density-functional theory now exists.

Physical Review A•Nov 22, 2002•25 citations

Note on the correlation energy of a many-fermion system

João da Providência

Nuclear Physics A•Aug 1, 1968•5 citations

Optimal Variational Method for Pair Correlations in Many-Fermion Systems

James C. Porter

By means of a suitably chosen variational principle, Euler equations are derived which generalize the Hartree-Fock equations in such a way as to include two-particle correlations. For a system of $N$ fermions these equations involve $N$ single-particle functions and $\frac{1}{2}N(N\ensuremath{-}1)$ pair correlation functions. The Euler equations are optimal in the sense that a more accurate estimation of the total energy would require the introduction of three-particle correlation functions and the retention of terms nonlinear in the two-particle functions. Although intended primarily for use in the calculation of atomic and molecular electronic structure, the Euler equations are here used to determine the Coulomb correlation energy in the case of the high-density electron gas. The result obtained is shown to have the same leading logarithmic divergence with density as that found previously by Gell-Mann and Brueckner.

Physical Review•Nov 1, 1965•3 citations
The method of correlated basis functions is used in the study of the ground-state properties of a one-dimensional system of bosons interacting through a repulsive $\ensuremath{\delta}$-function potential. Ground-state energies are determined numerically for intermediate values of the coupling constant in three steps: (1) a trial form of the radial distribution function generated by the Bijl-Dingle-Jastrow (BDJ) type of wave function is introduced to obtain approximate ground-state energies, (2) the paired-phonon analysis is applied to improve the BDJ description of the ground state, and (3) leading corrections to the improved approximate energies are evaluted from the second-order perturbation energy generated by the three-phonon vertex. The obtained energy values are found to agree closely with the exact results calculated by Lieb and Liniger.
In earlier work, expressions have been constructed for the single-particle kinetic-energy functional ${T}_{s}[\ensuremath{\rho}]$ for independent fermions subject to harmonic confinement in low dimensions, with $\ensuremath{\rho}$ the particle density. Here, the differential equation for $\ensuremath{\rho}$ is first obtained in d dimensions for an arbitrary number of closed shells. Then, by using the known Euler-Lagrange equation, the functional derivative $\ensuremath{\delta}{T}_{s}/\ensuremath{\delta}\ensuremath{\rho}(\mathbf{r})$ is constructed. ${T}_{s}[\ensuremath{\rho}]$ itself is proved to take the form of a linear combination of three pieces: (i) a von Weizs\"acker inhomogeneity kinetic energy, but with the original coefficient reduced by a dimensionality factor 1/d,1/d,1/d, (ii) a Thomas-Fermi kinetic energy, and (iii) a truly nonlocal contribution that, however, is shown to involve only the density $\ensuremath{\rho}$ itself and its first derivative. Thus, for this model, which is currently highly relevant to the interpretation of experiments on the evaporative cooling of dilute, and hence almost noninteracting, fermions, a complete density-functional theory now exists.
By means of a suitably chosen variational principle, Euler equations are derived which generalize the Hartree-Fock equations in such a way as to include two-particle correlations. For a system of NNN fermions these equations involve NNN single-particle functions and $\frac{1}{2}N(N\ensuremath{-}1)$ pair correlation functions. The Euler equations are optimal in the sense that a more accurate estimation of the total energy would require the introduction of three-particle correlation functions and the retention of terms nonlinear in the two-particle functions. Although intended primarily for use in the calculation of atomic and molecular electronic structure, the Euler equations are here used to determine the Coulomb correlation energy in the case of the high-density electron gas. The result obtained is shown to have the same leading logarithmic divergence with density as that found previously by Gell-Mann and Brueckner.