Temperature Effects in a Fermi Gas with Population Imbalance

Abstract

We investigate temperature effects in a Fermi gas with imbalanced spin populations. From the general expression of the thermal gap equation we find, in {\it weak coupling limit}, an analytical expression for the transition temperature $T_c$ as a function of various possibilities of chemical potential and mass asymmetries between the two particle species. For a range of asymmetry between certain specific values, this equation always has two solutions for $T_c$ which has been interpreted as a reentrant phenomena or a pairing induced by temperature effect. We show that the lower $T_c$ is never related to a stable solution. The same results are obtained in {\it strong coupling limit}. The thermodynamical potential is carefully analyzed to avoid the consideration of the unstable solutions. We also obtain the tricritical points for the chemical potential and mass imbalanced cases, and beyond these points we properly minimize the thermodynamic potential to find the stable and metastable first order transition lines.