The equation of state of the partially polarized two component Fermi gas at zero temperature in the unitary limit is computed by the ab initio auxiliary field Monte Carlo method. From this, we obtain the critical ratio of the chemical potentials ${\ensuremath{\mu}}_{\ensuremath{\downarrow}}∕{\ensuremath{\mu}}_{\ensuremath{\uparrow}}$ at the phase transitions. The value of ${\ensuremath{\mu}}_{\ensuremath{\downarrow}}∕{\ensuremath{\mu}}_{\ensuremath{\uparrow}}$ at the transition between the fully paired superfluid and the partially polarized phases is 0.11, while the critical value at the phase transition between the partially polarized phase and the fully polarized normal fluid is $\ensuremath{-}0.59$. We also determine the radial boundaries of the phase transitions of the Fermi gas in the harmonic trap as a function of the total polarization. We find that beyond the critical polarization 0.65, the fully paired superfluid core disappears in the trapped Fermi gas.
We study the transport properties of a Fermi gas with strong attractive interactions close to the unitary limit. In particular, we compute the spin diffusion lifetime of the Fermi gas due to superfluid fluctuations above the BCS transition temperature
Tc. To calculate the spin diffusion lifetime we need the scattering amplitudes. The scattering amplitudes are dominated by the superfluid fluctuations at temperatures just above
Tc. The normal scattering amplitudes are calculated from the Landau parameters. These Landau parameters are obtained from the local version of the induced interaction model for computing Landau parameters. We also calculate the leading order finite temperature correction to the diffusion lifetime. A calculation of the spin diffusion coefficient is presented in the end. Upon choosing a proper value of
F0a, we are able to present a good match between the theoretical result and the experimental measurement, which indicates the presence of the superfluid fluctuations near
Tc.
We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph, Elliott, and Thomas [Shear Viscosity of a Universal Fermi Gas Near the Superfluid Phase Transition, Phys. Rev. Lett. 115, 020401 (2015).PRLTAO0031-900710.1103/PhysRevLett.115.020401] and measurements of the equation of state by Ku et al. [Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).SCIEAS0036-807510.1126/science.1214987]. We find that the shear viscosity to particle density ratio just above the critical temperature is η/n|_{T_{c}}=0.41±0.11. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above T_{c} with η/s|_{min}=0.50±0.10.