The Fermionic Density-functional at Feshbach Resonance

Details The Fermionic Density-functional at Feshbach Resonance The Fermionic Density-functional at Feshbach Resonance

2007-04-05

arxiv.org/abs/0704.0769v1

Physics

Condensed Matter

Other Condensed Matter

Five pages, one table. accepted for publication in PRA

Scientific paper

10.1103/PhysRevA.75.052509

We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature.The atoms interact via a short range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second order perturbation theory, has the same density dependence as the first order exchange energy, and the two almost exactly cancel each other at Feshbach resonance irrespective of the shape of the potential, provided $(\mu r_s) >> 1$. Here $(\mu)^{-1}$ is the range of the two-body potential, and $r_s$ is defined through the number density $n=3/(4\pi r_s^3)$. The implications of this result for universality is discussed.

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