Phase Separation and an upper bound for $\Delta$ for Fermi fluids in the Phase Separation and an upper bound for $\Delta$ for Fermi fluids in the unitary regime

摘要

An upper bound is derived for $\Delta$ for a cold dilute fluid of equalamounts of two species of fermion in the unitary regime $k_f a \to \infty$(where $k_f$ is the Fermi momentum and $a$ the scattering length, and $\Delta$is a pairing energy: the difference in energy per particle between adding tothe system a macroscopic number (but infinitesimal fraction) of particles ofone species compared to adding equal numbers of both. The bound is $\delta \leq{5/3} (2 (2 \xi)^{2/5} - (2 \xi))$ where $\xi=\epsilon/\epsilon_{\rm FG}$,$\delta= 2 \Delta/\epsilon_{\rm FG}$; $\epsilon$ is the energy per particle and$\epsilon_{\rm FG}$ is the energy per particle of a noninteracting Fermi gas.If the bound is saturated, then systems with unequal densities of the twospecies will separate spatially into a superfluid phase with equal numbers ofthe two species and a normal phase with the excess. If the bound is notsaturated then $\Delta$ is the usual superfluid gap. If the superfluid gapexceeds the maximum allowed by the inequality phase separation occurs.