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

Abstract

An upper bound is derived for $\Delta$ for a cold dilute fluid of equal amounts 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 to the system a macroscopic number (but infinitesimal fraction) of particles of one species compared to adding equal numbers of both. The bound is $\delta \le 5/3(2(2\xi {)}^{2/5}-(2\xi ))$ where $\xi =\epsilon /{\epsilon }_{\mathrm{FG}}$, $\delta =2\Delta /{\epsilon }_{\mathrm{FG}}$; $\epsilon$ is the energy per particle and ${\epsilon }_{\mathrm{FG}}$ is the energy per particle of a noninteracting Fermi gas. If the bound is saturated, then systems with unequal densities of the two species will separate spatially into a superfluid phase with equal numbers of the two species and a normal phase with the excess. If the bound is not saturated then $\Delta$ is the usual superfluid gap. If the superfluid gap exceeds the maximum allowed by the inequality phase separation occurs.

This is the version to be publishd. The notation has been improved to match standard useage. An improved discussion on the implication of the nature of the bound and the physical meaning of the parameter Delta

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• Finite Temperature Phase Diagram of a Two-Component Fermi Gas with Density Imbalance
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• Quantum liquid-crystal order in resonant atomic gases
• Ground state energy of unitary fermion gas with the Thomson Problem approach
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• Feasibility of a Fulde-Ferrell-Larkin-Ovchinnikov superfluid Fermi atomic gas
• Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities
• Critical Zeeman Splitting of a Unitary Fermi Superfluid
• Equation of State and Phases of Polarized Unitary Fermi Gas
• Phase diagrams of neutron-proton superfluid in asymmetric nuclear matter