Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas

The first detailed comparison between ab initio calculations of finite fermionic superfluid systems, performed recently by Chang and Bertsch [Phys. Rev. A 76, 021603(R), (2007)] and by von Stecher, Greene and Blume [e-print arXiv:00705:0671v1], and the extension of the density functional theory Superfluid Local Density Approximation (SLDA) is presented. It is shown that SLDA reproduces the total energies, number density distributions in inhomogeneous systems along with the energy of the normal state in homogeneous systems. Unlike the Kohn-Sham LDA, in SLDA the effective fermion mass differs from the bare fermion mass and the spectrum of elementary excitations is also reproduced.