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

article

2002
Lancaster, Pa
, 2002

Physics

Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015

66(2002)
:5
, p. 054501,1-054501,4

1094-1622

1050-2947

054501

E-only publicatie

English (eng)

University of Antwerp

In earlier work, expressions have been constructed for the single-particle kinetic-energy functional T-s[rho] for independent fermions subject to harmonic confinement in low dimensions, with rho the particle density. Here, the differential equation for 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 deltaT(s)/deltarho(r) is constructed. T-s[rho] itself is proved to take the form of a linear combination of three pieces: (i) a von Weizsacker 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 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.

https://repository.uantwerpen.be/docman/irua/b4596c/2066.pdf

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