Open AccessDensity functional theory of the trapped Fermi gas in the unitary regime
Author(s) -
van Zyl B.P.,
Hutchinson D.A.W.
Publication year - 2008
Publication title -
laser physics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.59
H-Index - 72
eISSN - 1612-202X
pISSN - 1612-2011
DOI - 10.1002/lapl.200710091
Subject(s) - unitary state , physics , fermi gas , density functional theory , fermi gamma ray space telescope , limit (mathematics) , work (physics) , thomas–fermi model , quantum mechanics , energy (signal processing) , functional theory , statistical physics , mathematical analysis , mathematics , political science , law , electron
We investigate a density‐functional theory (DFT) approach for an unpolarized trapped dilute Fermi gas in the unitary limit. A reformulation of the recent work of T. Papenbrock [1] in the language of fractional exclusion statistics allows us to obtain an estimate of the universal factor, ξ 3 D , in three dimensions (3D), in addition to providing a systematic treatment of finite‐ N corrections. We show that in 3D, finite‐ N corrections lead to unphysical values for ξ 3 D , thereby suggesting that a simple DFT applied to a small number of particles may not be suitable in 3D. We then perform an analogous calculation for the two dimensional (2D) system in the infinite‐scattering length regime, and obtain a value of ξ 2 D = 1. Owing to the unique properties of the Thomas‐Fermi energy density‐functional in 2D our result, in contrast to 3D, is exact and therefore requires no finite‐ N corrections. (© 2007 by Astro Ltd., Published exclusively by WILEY‐VCH Verlag GmbH & Co. KGaA)