Collective oscillations of a classical gas confined in harmonic traps

Starting from the Boltzmann equation, we calculate the frequency and the damping of the collective oscillations of a classical gas confined by a harmonic potential. Both the monopole and quadrupole modes are considered in the presence of spherical as well as axially deformed traps. The relaxation time is calculated using a Gaussian ansatz which explicitly accounts for the occurence of quadrupole deformations in velocity space. Our approach provides an explicit description of the transition between the hydrodynamic and collisionless regimes. The predictions are in very good agreement with the results of a molecular-dynamics simulation carried out in a gas of hard spheres.