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We determine the energy density $xi (3/5) n epsilon_F$ and the gradient correction $lambda hbar^2( abla n)^2/(8m n)$ 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.
We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the $p$-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, $p$-wave scattering le
Weak attractive interactions in a spin-imbalanced Fermi gas induce a multi-particle instability, binding multiple fermions together. The maximum binding energy per particle is achieved when the ratio of the number of up- and down-spin particles in th
Using the $hbar$-expansion of the Greens function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and the spin-or
We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give ana
We probe the superconducting gap in the zero temperature ground state of an attractively interacting spin-imbalanced two-dimensional Fermi gas with Diffusion Monte Carlo. A condensate fraction at nonzero pair momentum evidences a spatially non-unifor