Collisional damping of the collective oscillations of a trapped Fermi gas

We consider a Fermi gas confined by a harmonic trapping potential and we highlight the role of the Fermi-Dirac statistics by studying frequency and damping of collective oscillations of quadrupole type in the framework of the quantum Boltzmann equation, in which statistical corrections are taken into account in the collisional integral. We are able to describe the crossover from the collisionless regime to the hydrodynamic one by introducing a temperature-dependent relaxation time $\tau_Q$. We show that, in the degenerate regime, the relaxation rate $1/\tau_Q$ exhibits a temperature dependence different from the collision rate $\gamma$. We finally compare the collisional properties of the Fermi gas with the ones of the Bose gas for temperatures above the Bose-Einstein condensation.