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 $P_C=[1-(1-\xi {)}^{6/5}]/[1+(1-\xi {)}^{6/5}]\doteq 0.34$. The $\xi =4/9$ defines the ratio of the symmetric ground state energy density to that of the ideal fermion gas.

Comments: Minor changes with typos corrected