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 Letters

Giant Fluctuations in a Degenerate Fermi Gas

Walter Kohn, Stephen J. Nettel

Published Jul 1, 1960• 53 citations
Publisher

Abstract

It was suggested that the ground stute of an interacting gas of fermions has giart density or spin-density fluctuations and that the Hartree and Hartree- Fcck equations of a one-dimensional gas have solutions which give lower enengies than customary plane wave solutions. Arguments are set forth for the view that for sufficiently weak interactions the Hartree (and Hartree-Fcck) ground stutes in two or more dimensions are the familiar plane wave states. It is concluded that for weak interactions the Hartree equations have a nontnivial ground stute only in one dimension. There is little doubt that this is also tnne for the HartreeFock equation. (B.O.G.)

DOI
10.1103/physrevlett.5.8

Related papers

Structure of Nuclear Matter

A. W. Overhauser

Equations for explicit Hartree states of energy lower than that of conventional ground states for noninteracting Fermi gases are given for Fermi gases with attractive interactions. One-dimensional and three-dimensional cases are treated. Large static density waves are shown to exist in such Fermi gases, and the binding energy is derived therefrom. If the density waves are used with the variational theorem, their contribution to the binding energy is greater, and it is concluded that density waves are of great importance in nuclear matter. In the limit of weak attractive interactions, the Fermi surface will become a manyfaced polyhedron, each pair of opposite faces arising from a density wave. (D.L.C.)

Physical Review Letters•Apr 15, 1960•173 citations

Hartree-Fock phase diagram of the two-dimensional electron gas

B. Bernu, Fran�ois Delyon, Markus Holzmann +1 more

We calculate the ground-state phase diagram of the homogeneous electron gas in two dimensions within the Hartree-Fock approximation. At high density, we find stable solutions, where the electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons, whereas the commensurate Wigner crystal is favored at lower densities, ${r}_{s}\ensuremath{\gtrsim}1.22$. Our explicit calculations demonstrate that the homogeneous Fermi-liquid state, though being an exact stationary solution of the Hartree-Fock equations, is never the Hartree-Fock ground state of the electron gas.

arXiv:1106.2939•Physical Review B•Sep 15, 2011•28 citations

Generalized Fermi sea for plane-wave Hartree-Fock theory: One dimensional model calculation

MANUEL DE LLANO, James P. Vary

The Hartree-Fock theory for many fermions with plane-wave orbitals but with abnormal occupation is studied. A one-dimensional problem with an interparticle interaction of finite range which saturates the $N$ body system at a fixed density and finite binding energy is solved explicitly. A direct variation of the resulting Hartree-Fock energy with respect to the additional variational parameters introduced is carried out numerically and results reminiscent of a gas-to-liquid phase transition are found.NUCLEAR STRUCTURE plane-wave Hartree-Fock; model calculation; nuclear matter.

Physical Review C•Mar 1, 1979•37 citations

Stability of the Plane Wave Hartree-Fock Ground State

Fumiaki Iwamoto, K. Sawada

The condition that the plane wave state is the lowest Hartree-Fock state of a large fermion system with repulsive interactions, is generally investigated and applied to the systems with $\ensuremath{\delta}$-type interactions, finite-range interactions, and long-range Coulomb interactions. It is found that for finite-range interactions the plane wave state is stable in both the high-density and low-density regions, but may become unstable in the intermediate-density region. The high-density stable region disappears for $\ensuremath{\delta}$-type interactions, while the low-density stable region vanishes for long-range Coulomb interactions. Especially for an electron gas, the critical value ${r}_{s}$ is smaller than 4.5. A speculation concerning the transition of the true ground state is discussed.

Physical Review•May 1, 1962•27 citations

Low-density Hartree-Fock solutions for a one-dimensional gas with attractive delta-function interactions

Gonzalo Gutiérrez, Angel Ricardo Plastino, G. Zannoli

New Hartree-Fock (HF) solutions are presented for a one-dimensional gas with attractive delta-function interactions. They are found by recourse to the variational principle and have, as special limiting cases, both the exact, zero-density HF solution and the plane-wave orbitals.

Physical Review A•Mar 1, 1981•0 citations

Generalized Fermi sea for plane-wave Hartree-Fock theory. II. Semi-realistic interactions in three dimensions

Valdir C. Aguilera-Navarro, Robert Hartman Belehrad, MANUEL DE LLANO +3 more

The possibility of abnormally occupying plane-wave Hartree-Fock determinants is studied analytically for several many-fermion systems interacting with short- and long-ranged pair potentials in three dimensions. Lower energy states are found in some cases, but they always depend sensitively on the shape of the potential as well as on the amount of space exchange present in the interaction.NUCLEAR STRUCTURE Plane-wave Hartree-Fock, nuclear matter.

Physical Review C•Sep 1, 1980•11 citations
It was suggested that the ground stute of an interacting gas of fermions has giart density or spin-density fluctuations and that the Hartree and Hartree- Fcck equations of a one-dimensional gas have solutions which give lower enengies than customary plane wave solutions. Arguments are set forth for the view that for sufficiently weak interactions the Hartree (and Hartree-Fcck) ground stutes in two or more dimensions are the familiar plane wave states. It is concluded that for weak interactions the Hartree equations have a nontnivial ground stute only in one dimension. There is little doubt that this is also tnne for the HartreeFock equation. (B.O.G.)
Equations for explicit Hartree states of energy lower than that of conventional ground states for noninteracting Fermi gases are given for Fermi gases with attractive interactions. One-dimensional and three-dimensional cases are treated. Large static density waves are shown to exist in such Fermi gases, and the binding energy is derived therefrom. If the density waves are used with the variational theorem, their contribution to the binding energy is greater, and it is concluded that density waves are of great importance in nuclear matter. In the limit of weak attractive interactions, the Fermi surface will become a manyfaced polyhedron, each pair of opposite faces arising from a density wave. (D.L.C.)
We calculate the ground-state phase diagram of the homogeneous electron gas in two dimensions within the Hartree-Fock approximation. At high density, we find stable solutions, where the electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons, whereas the commensurate Wigner crystal is favored at lower densities, ${r}_{s}\ensuremath{\gtrsim}1.22$. Our explicit calculations demonstrate that the homogeneous Fermi-liquid state, though being an exact stationary solution of the Hartree-Fock equations, is never the Hartree-Fock ground state of the electron gas.
The Hartree-Fock theory for many fermions with plane-wave orbitals but with abnormal occupation is studied. A one-dimensional problem with an interparticle interaction of finite range which saturates the NNN body system at a fixed density and finite binding energy is solved explicitly. A direct variation of the resulting Hartree-Fock energy with respect to the additional variational parameters introduced is carried out numerically and results reminiscent of a gas-to-liquid phase transition are found.NUCLEAR STRUCTURE plane-wave Hartree-Fock; model calculation; nuclear matter.
The condition that the plane wave state is the lowest Hartree-Fock state of a large fermion system with repulsive interactions, is generally investigated and applied to the systems with $\ensuremath{\delta}$-type interactions, finite-range interactions, and long-range Coulomb interactions. It is found that for finite-range interactions the plane wave state is stable in both the high-density and low-density regions, but may become unstable in the intermediate-density region. The high-density stable region disappears for $\ensuremath{\delta}$-type interactions, while the low-density stable region vanishes for long-range Coulomb interactions. Especially for an electron gas, the critical value rs{r}_{s}rs​ is smaller than 4.5. A speculation concerning the transition of the true ground state is discussed.