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

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

2006-10-10

arxiv.org/abs/cond-mat/0610256v1

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

10.1103/PhysRevA.76.025601

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 [Phys. Rev. A, {\bf 72}, 041602(R) (2005)] in the language of fractional exclusion statistics allows us to obtain an estimate of the universal factor, $\xi_{3D}$, 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 $\xi_{3D}$, 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 $\xi_{2D}=1$. Owing to the unique properties of the Thomas-Fermi energy density-functional in 2D our result, in contrast to 3D, is {\em exact} and therefore requires no finite-$N$ corrections.

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