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 A

Equations satisfied by the kinetic-energy functional and its derivatives

Daniel P. Joubert

Published Oct 1, 1994• 3 citations
Publisher

Abstract

A set of equations that the kinetic-energy functional of a system of noninteracting fermions and its derivatives must satisfy are derived. These complement the hierarchy of equations derived by Kugler [Phys. Rev. A 41, 3489 (1990)]. As a consequence of these equations the kinetic energy can be expressed in terms of any of its functional derivatives.

DOI
10.1103/physreva.50.3527

Related papers

EXACT KINETIC ENERGY FUNCTIONAL OF NONINTERACTING FERMIONS

Jiushu Shao

The exact expression of kinetic energy as a functional of the density for a system of noninteracting fermions, which has been searched for many years, is derived based on the direct method.

Modern Physics Letters B•Aug 10, 1993•13 citations

Homogeneity and isotropy of space requisites for kinetic-energy functional derivatives

Daniel P. Joubert

Homogeneity and isotropy of space lead to two hierarchies of equations for the independent Fermion kinetic-energy functional Ts[n]. The hierarchies link the mth functional derivative of Ts[n] to the (m+1)th functional derivative. The constraints imposed on Ts[n] are different for nonlocal functionals but equivalent for local functionals. As a consequence of the first hierarchy, Ts[n] can be expressed in terms of any of its functional derivatives.

The Journal of Chemical Physics•Dec 1, 1994•4 citations

The kinetic-energy functional of a one-dimensional system of fermions

V.Iu. Kolmanovich, I. M. Reznik

Soviet physics. Doklady•Jun 1, 1981•0 citations

Exact hierarchy of equations for the kinetic energy functional

Alfred A. Kugler

The virial theorem is used to derive an exact hierarchy of coupled equations for the kinetic energy functional T[\ensuremath{\rho}] of an inhomogeneous system of noninteracting fermions. The hierarchy links the nth functional derivative of T[\ensuremath{\rho}] with respect to the particle density \ensuremath{\rho}(r) to the (n+1)th functional derivative and to \ensuremath{\rho}(r) for n=1,2,. . . . These functional derivatives are the analogs of the so-called ``direct correlation functions'' in the theory of classical fluids, and the hierarchy obtained resembles the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the distribution functions associated with such fluids. Some general properties of the two- and three-point correlation functions are described, in particular, their relations to the linear and quadratic response functions that describe the response of the inhomogeneous system to a change in the potential. The hierarchy is then used to obtain several equivalent expressions for T[\ensuremath{\rho}], one of which is an infinite series of successively higher-order terms, of which the nth term represents the contribution from the n-point correlation function and the densities associated with those points. The equations are then examined in the homogeneous (uniform) gas limit and the first and second equations are verified explicitly with the aid of the associated response functions. The analysis indicates that the infinite series expression converges rapidly for the three-dimensional gas; it also reveals that for both the one-dimensional and two-dimensional gas, the series terminates after the first few terms, suggesting that the structure of T[\ensuremath{\rho}] is much simpler in one and two dimensions than in three dimensions.

Physical Review A•Apr 1, 1990•28 citations

Kinetic Equations for Quantum Many-Particle Systems

Herbert E. Spohn

The current status of the derivation of kinetic equations from quantum many-particle dynamics is reviewed.

arXiv:0706.0807•Jun 6, 2007•11 citations

Equal-time hierarchies for transport descriptions of fermionic fields

R.A. Ionescu, H.H. Wolter

A transport theory which is not restricted to the gradient and quasi-particle approximations is presented which is formulated in terms of the energy moments, or equivalently the equal-time derivatives of the one-particle Green functions. A set of infinite hierarchies of kinetic and constraint equations for equal-time quantities for the spectral and the kinetic part of the one-particle Green function are derived. The hierarchies for the spectral function truncate automatically as in the mean field approximation. The possibility of a systematic truncation of the hierarchies for the kinetic part is discussed. The effects the quantum corrections are illustrated in a simple one-dimensional model.

arXiv:nucl-th/0009022•Sep 7, 2000•0 citations
A set of equations that the kinetic-energy functional of a system of noninteracting fermions and its derivatives must satisfy are derived. These complement the hierarchy of equations derived by Kugler [Phys. Rev. A 41, 3489 (1990)]. As a consequence of these equations the kinetic energy can be expressed in terms of any of its functional derivatives.
The virial theorem is used to derive an exact hierarchy of coupled equations for the kinetic energy functional T[\ensuremath{\rho}] of an inhomogeneous system of noninteracting fermions. The hierarchy links the nth functional derivative of T[\ensuremath{\rho}] with respect to the particle density \ensuremath{\rho}(r) to the (n+1)th functional derivative and to \ensuremath{\rho}(r) for n=1,2,. . . . These functional derivatives are the analogs of the so-called ``direct correlation functions'' in the theory of classical fluids, and the hierarchy obtained resembles the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the distribution functions associated with such fluids. Some general properties of the two- and three-point correlation functions are described, in particular, their relations to the linear and quadratic response functions that describe the response of the inhomogeneous system to a change in the potential. The hierarchy is then used to obtain several equivalent expressions for T[\ensuremath{\rho}], one of which is an infinite series of successively higher-order terms, of which the nth term represents the contribution from the n-point correlation function and the densities associated with those points. The equations are then examined in the homogeneous (uniform) gas limit and the first and second equations are verified explicitly with the aid of the associated response functions. The analysis indicates that the infinite series expression converges rapidly for the three-dimensional gas; it also reveals that for both the one-dimensional and two-dimensional gas, the series terminates after the first few terms, suggesting that the structure of T[\ensuremath{\rho}] is much simpler in one and two dimensions than in three dimensions.
A transport theory which is not restricted to the gradient and quasi-particle approximations is presented which is formulated in terms of the energy moments, or equivalently the equal-time derivatives of the one-particle Green functions. A set of infinite hierarchies of kinetic and constraint equations for equal-time quantities for the spectral and the kinetic part of the one-particle Green function are derived. The hierarchies for the spectral function truncate automatically as in the mean field approximation. The possibility of a systematic truncation of the hierarchies for the kinetic part is discussed. The effects the quantum corrections are illustrated in a simple one-dimensional model.