Low temperatures shear viscosity of a two-component dipolar Fermi gas with unequal population

By using the Green's functions method and linear response theory we calculate the shear viscosity of a two-component dipolar Fermi gas with population imbalance (spin polarized) in the low temperatures limit. In the strong-coupling Bose-Einstein condensation (BEC) region where a Feshbach resonance gives rise to tightly bound dimer molecules, a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions (atoms). The interactions between dimer-atom, dimer-dimer, and atom-atom take into account to the viscous relaxation time (τη). By evaluating the self-energies in the ladder approximation we determine the relaxation times due to dimer-atom (τDA), dimer-dimer (τcDD,τdDD), and atom-atom (τAA) interactions. We will show that relaxation rates due to these interactions τDA−1,τcDD−1, τdDD−1, and τAA−1 have T2, T4, e−E/kBT (E is the spectrum of the dimer atoms), and T3/2 behavior respectively in the low temperature limit (T→0) and consequently, the atom-atom interaction plays the dominant role in the shear viscosity in this rang of temperatures. For small polarization (τDA,τAA≫τcDD,τdDD), the low temperatures shear viscosity is determined by contact interaction between dimers and the shear viscosity varies as T−5 which has the same behavior as the viscosity of other superfluid systems such as superfluid neutron stars, and liquid helium.