Density functional theory of the trapped Fermi gas in the unitary regime

Abstract

We investigate a density-functional theory (DFT) approach for an unpolarized trapped dilute Fermi gas in the unitary limit . A reformulation of the recent work of T. Papenbrock [Phys. Rev. A, {\bf 72}, 041602(R) (2005)] in the language of fractional exclusion statistics allows us to obtain an estimate of the universal factor, ${\xi }_{3D}$, in three dimensions (3D), in addition to providing a systematic treatment of finite-$N$ corrections. We show that in 3D, finite-$N$ corrections lead to unphysical values for ${\xi }_{3D}$, thereby suggesting that a simple DFT applied to a small number of particles may not be suitable in 3D. We then perform an analogous calculation for the two-dimensional (2D) system in the infinite-scattering length regime, and obtain a value of ${\xi }_{2D}=1$. Owing to the unique properties of the Thomas-Fermi energy density-functional in 2D our result, in contrast to 3D, is {\em exact} and therefore requires no finite-$N$ corrections.

References in corpus (21)

• Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Pairing and Phase Separation in a Polarized Fermi Gas
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Superfluid Fermi Gases with Large Scattering Length
• Universal Thermodynamics of Degenerate Quantum Gases in the Unitarity Limit
• Heat Capacity of a Strongly-Interacting Fermi Gas
• Measurement of positive and negative scattering lengths in a Fermi gas of atoms
• Fermi systems with long scattering lengths
• Spin 1/2 Fermions in the Unitary Regime: A Superfluid of a New Type
• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Virial Theorem and Universality in a Unitary Fermi Gas
• Evaporative Cooling of a Two-Component Degenerate Fermi Gas
• Formation Time of a Fermion Pair Condensate
• Fermi gas near unitarity around four and two spatial dimensions
• Momentum distribution of a Fermi gas of atoms in the BCS-BEC crossover
• Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap
• Density-functional theory for fermions in the unitary regime
• Formation of a vortex lattice in a rotating BCS Fermi gas
• Finite Temperature Momentum Distribution of a Trapped Fermi Gas
• Ground state energy of unitary fermion gas with the Thomson Problem approach

Cited by in corpus (2)

• Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas
• Surface Effects in the Unitary Fermi Gas