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Density functional theory of the trapped Fermi gas in the unitary regime

✍ Scribed by B.P. van Zyl; D.A.W. Hutchinson

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 122 KB
Volume: 5
Category: Article
ISSN: 1612-2011
DOI: 10.1002/lapl.200710091

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✦ Synopsis

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~3D~, 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~3D~, 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~2D~=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.

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