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

@misc{citeulike:893430, abstract = {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.}, author = {van Zyl, Brandon P. and Hutchinson, D. A. W. and Need, Melodie }, citeulike-article-id = {893430}, eprint = {cond-mat/0610256}, keywords = {dft}, month = {Oct}, posted-at = {2006-10-11 17:05:13}, priority = {2}, title = {Density functional theory of the trapped Fermi gas in the unitary regime}, url = {http://arxiv.org/abs/cond-mat/0610256}, year = {2006} }

TY - ELEC ID - citeulike:893430 L3 - citeulike-article-id:893430 TI - Density functional theory of the trapped Fermi gas in the unitary regime N2 - 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. KW - dft AU - van Zyl, Brandon AU - Hutchinson, DAW AU - Need, Melodie PY - 2006/Oct/10/ UR - http://arxiv.org/abs/cond-mat/0610256 ER -