Extended Thomas-Fermi density functional for the unitary Fermi gas

Abstract

Erratum: Extended Thomas-Fermi density functional for the unitary Fermi gas [Phys. Rev. A 78, 053626 (2008) We determine the energy density ξ(3/5)nεF and the gradient correction λh 2 (∇n) 2 /(8m n) of the extended Thomas-Fermi (ETF) density functional, where n is number density and εF 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. 99, 233201 (2007)]. In particular we find that ξ = 0.455 and λ = 0.13 give the best fit of the DMC data with an even number N of particles. We also study the odd-even splitting γN 1/9h ω of the ground-state energy for the unitary gas in a harmonic trap of frequency ω determining the constant γ. Finally we investigate the effect of the gradient term in the time-dependent ETF model by introducing generalized Galilei-invariant hydrodynamics equations.

Collective modes in the anisotropic unitary Fermi gas and the inclusion of a backflow term

“…The extended Lagrangian density of dilute and ultracold superfluids is given by [1][2][3][4][5][6][7][8] …”

“…where ξ 0.4 is a universal parameter [1,2,16,26,27] and various approaches [1,2,16,19,26,27] suggest that λ 0.25. The local chemical potential is then…”

“…In this paper we calculate the collective monopole and quadrupole modes of the unitary Fermi gas (characterized by an infinite s-wave scattering length) under axially symmetric anisotropic harmonic confinement by using the extended Lagrangian density of superfluids, which we proposed a few years ago [1], to study the unitary Fermi gas [1][2][3][4][5][6][7][8]. The internal energy density of our extended Lagrangian density contains a term proportional to the kinetic energy of a uniform noninteracting gas of fermions, plus a gradient correction of the von-Weizsacker form λh 2 /(8m)(∇n/n) 2 [9].…”

dc Josephson effect with Fermi gases in the Bose-Einstein regime

“…In fact, we have recently shown that at unitarity (y = 0) the superfluid NLSE of Eq. (4) must be modified with the inclusion of an additional nonlinear term [34]. Nevertheless, this beyond-mean-field term goes to zero for a large number of atoms.…”

Fulde-Ferrell states and Berezinskii-Kosterlitz-Thouless phase transition in two-dimensional imbalanced Fermi gases

“…Since the strong phase fluctuations destroying the quasi-long-range order and phase coherence result in a breakdown of the spin-wave approximation of the fluctuation action, an improved study of the FF state at finite temperatures should take into account the fluctuations more completely. We note, as an interesting line of research, that a dispersion relation for collective excitations including higher-order terms ∝q 4 has been introduced for unitary Fermi gases by Salasnich et al [77] and applied at the finite (low) temperature in Ref. [78].…”