Density Functional Theory for non-relativistic Fermions in the Unitarity Limit

Abstract

We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d=4-epsilon spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E=E_(LDA)(1+c_s (3N)^(-2/3)), where E_(LDA) is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find c_s=1.68, which is significantly larger than the result for non-interacting fermions, c_s=0.5.

17 pages, final version, Nuclear Physics A, in press

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Cited by in corpus (13)

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• Self-interaction errors in nuclear energy density functionals
• Effective-Range Dependence of Resonantly Interacting Fermions
• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• DC Josephson Effect with Fermi gases in the Bose-Einstein regime
• Predicting Energies of Small Clusters from the Inhomogeneous Unitary Fermi Gas
• Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound
• Ground-state energy of the unitary Fermi gas from the epsilon expansion
• Gradient corrections to the local density approximation for trapped superfluid Fermi gases
• Dynamical properties of the unitary Fermi gas: collective modes and shock waves
• Dispersive effects in the unitary Fermi gas
• Comment on "Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas"
• Anomalous dispersion of the collective modes of an ultracold ${}^{6}Li-$ ${}^{40}K$ mixture in a square optical lattice