Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas

Details Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas

2008-09-10

arxiv.org/abs/0809.1820v3

Phys. Rev. A 78, 053626 (2008)

Physics

Condensed Matter

Other Condensed Matter

7 pages, 3 figures, 1 table; corrected some typos; published in Phys. Rev. A; added erratum: see also the unpublished diploma

Scientific paper

10.1103/PhysRevA.78.053626

We determine the energy density $\xi (3/5) n \epsilon_F$ and the gradient correction $\lambda \hbar^2(\nabla n)^2/(8m n)$ of the extended Thomas-Fermi (ETF) density functional, where $n$ is number density and $\epsilon_F$ is Fermi energy, for a trapped two-components Fermi gas with infinite scattering length (unitary Fermi gas) on the basis of recent diffusion Monte Carlo (DMC) calculations [Phys. Rev. Lett. {\bf 99}, 233201 (2007)]. In particular we find that $\xi=0.455$ and $\lambda=0.13$ give the best fit of the DMC data with an even number $N$ of particles. We also study the odd-even splitting $\gamma N^{1/9} \hbar \omega$ of the ground-state energy for the unitary gas in a harmonic trap of frequency $\omega$ determining the constant $\gamma$. Finally we investigate the effect of the gradient term in the time-dependent ETF model by introducing generalized Galilei-invariant hydrodynamics equations.

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