Abstract:
To review the fermionic quasi particle branch of superfluid Fermi gases in the Bardeen-Cooper
Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover at nonzero temperature and in the
temperature range below the transition temperature in the Gaussian pair fluctuation approximation. The
Gaussian pair fluctuation at low wave number and energy proportional to wave number, to derive an explicit
dispersion equation for the nonzero-temperature complex sound velocity. This project is deal about the
coupling of these modes to the fermionic continuum of quasi particle-quasi hole excitations by performing a
non-perturbative analytic continuation of the pairing field propagator. At nonezero temperature, to recover the
known exponential temperature dependence of the damping rate and velocity shift of the AndersonBogoliubov branch. In the vicinity of Tc, we find analytically a weakly-damped collective mode whose
velocity vanishes with a critical exponent of 1/2, and whose quality factor diverges logarithmically with Tc −
T, there by clarifying an existing debate in the literature. The process of a bsorption or emission of a bosonic
collective excitation by a fermionic quasi particle in asuperfluid of paired fermions. From the random phase
approximation equation of motion of the bosonic excitation annihilation operator, we obtain an expression of
the coupling amplitude of this process, which is limited neither to resonant processes nor to the long
wavelength limit
