Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities

Abstract

A quasi-Gaussian approximation scheme is formulated to study the strongly correlated imbalanced fermions thermodynamics, where the mean-field theory is not applicable. The non-Gaussian correlation effects are understood to be captured by the statistical geometric mean of the individual susceptibilities. In the three-dimensional unitary fermions ground state, an {\em universal} non-linear scaling transformation relates the physical chemical potentials with the individual Fermi kinetic energies. For the partial polarization phase separation to full polarization, the calculated critical polarization ratio is $P_C={[1-(1-ξ)^{6/5}]}/{[1+(1-ξ)^{6/5}]}\doteq 0.34$. The $ξ=4/9$ defines the ratio of the symmetric ground state energy density to that of the ideal fermion gas.