Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas

Abstract

We determine the energy density $\xi (3/5)n{\epsilon }_F$ and the gradient correction $\lambda {\hslash }^2(\nabla n{)}^2/(8mn)$ 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 $\gamma N^{1/9}\hslash \omega$ 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.

7 pages, 3 figures, 1 table; corrected some typos; published in Phys. Rev. A; added erratum: see also the unpublished diploma thesis of Marco Manzoni (supervisors: N. Manini and L. Salasnich) at http://www.mi.infm.it/manini/theses/manzoni.pdf

References in corpus (19)

• Theory of ultracold Fermi gases
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Collective excitations of a degenerate gas at the BEC-BCS crossover
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Epsilon expansion for a Fermi gas at infinite scattering length
• Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
• Universal properties of a trapped two-component Fermi gas at unitarity
• Formation Time of a Fermion Pair Condensate
• Fermi gas near unitarity around four and two spatial dimensions
• Unitary Fermi Gas in a Harmonic Trap
• BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
• Density-functional theory for fermions in the unitary regime
• Macroscopic Periodic Tunneling of Fermi Atoms in the BCS-BEC Crossover
• Kirzhnits gradient expansion for a D-dimensional Fermi gas
• Expansion of a Fermi Cloud in the BCS-BEC Crossover
• Collective Excitations of Strongly Interacting Fermi Gases of Atoms in a Harmonic Trap
• Density functional theory for fermions close to the unitary regime
• Hydrodynamic Modes in a Trapped Strongly Interacting Fermi Gases of Atoms
• Density functional theory of the trapped Fermi gas in the unitary regime

Cited by in corpus (56)

• Applications of quantum Monte Carlo methods in condensed systems
• Few-body physics with ultracold atomic and molecular systems in traps
• Resonantly Interacting Fermions In a Box
• Quantized Superfluid Vortex Rings in the Unitary Fermi Gas
• Effective-Range Dependence of Resonantly Interacting Fermions
• DC Josephson Effect with Fermi gases in the Bose-Einstein regime
• Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials
• Thermal Conductivity and Sound Attenuation in Dilute Atomic Fermi Gases
• Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
• Bose-Einstein condensation: Twenty years after
• Fulde-Ferrell states and Berezinskii-Kosterlitz-Thouless phase transition in two-dimensional imbalanced Fermi gases
• Hydrodynamics of Bose and Fermi superfluids at zero temperature: the superfluid nonlinear Schrodinger equation
• Shock waves in strongly interacting Fermi gas from time-dependent density functional calculations
• Supersonic and subsonic shock waves in the unitary Fermi gas
• Rotating quantum turbulence in the unitary Fermi gas
• Validating Simple Dynamical Simulations of the Unitary Fermi Gas
• Fermionic shock waves - dissipative or dispersive?
• Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas
• Strength of the Vortex-Pinning Interaction from Real-Time Dynamics
• Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound
• Trapped unitary two-component Fermi gases with up to ten particles
• Dark solitons dynamics and snake instability in superfluid Fermi gases trapped by an anisotropic harmonic potential
• Effective field theory and dispersion law of the phonons of a non-relativistic superfluid
• Ground-state densities of repulsive two-component Fermi gases
• Phononic collective excitations in superfluid Fermi gases at nonzero temperatures
• DC and AC Josephson effects with superfluid Fermi atoms across a Feshbach resonance
• Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures
• Surface Effects in the Unitary Fermi Gas
• Viscosity-entropy ratio of the unitary Fermi gas from zero-temperature elementary excitations
• Beliaev damping of the Goldstone mode in atomic Fermi superfluids
• Gradient corrections to the local density approximation for trapped superfluid Fermi gases
• Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit
• Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials
• Bell Soliton in Ultra-cold Atomic Fermi Gas
• Dynamical properties of the unitary Fermi gas: collective modes and shock waves
• Collective modes in the anisotropic unitary Fermi gas and the inclusion of a backflow term
• Stability and collapse of fermions in a binary dipolar boson-fermion 164Dy-161Dy mixture
• Shock waves in a quasi one-dimensional Bose-Einstein condensate
• Quantum Chaos for the Unitary Fermi Gas from the Generalized Boltzmann Equations
• Stability of trapped degenerate dipolar Bose and Fermi gases
• On the kinetic energy of unitary Fermi gas in a harmonic trap
• Dynamics of shock waves in a superfluid unitary Fermi gas
• Goldstone and Higgs Hydrodynamics in the BCS-BEC Crossover
• Electrodynamics of superconductors: from Lorentz to Galilei at zero temperature
• Crow instability in unitary Fermi gas
• Transition from supersonic to subsonic waves in superfluid Fermi gases
• Critical velocity, vortex shedding and drag in a unitary Fermi superfluid
• Dispersive effects in the unitary Fermi gas
• Dark solitons in the unitary Bose gas
• Unitary Fermi superfluid near the critical temperature: thermodynamics and sound modes from elementary excitations
• Study of a degenerate dipolar Fermi gas of 161Dy atoms
• Correlations and synchronization in a Bose-Fermi mixture
• Vortex-lattice structures in rotating Bose-Fermi superfluid mixtures
• Superfluid hydrodynamics of polytropic gases:dimensional reduction and sound velocity
• Schrödinger-Navier-Stokes equation for capillary fluids
• Density of states for the Unitary Fermi gas and the Schwarzschild black hole