Collisionless dynamics of dilute Bose gases: Role of quantum and thermal fluctuations - art. no. 063615

We study the low-energy collective oscillations of a dilute Bose gas at fin ite temperature in the collisionless regime. By using a lime-dependent mean -field scheme we derive for the dynamics of the condensate and noncondensat e components a set of coupled equations, which we solve perturbatively to s econd order in the interaction coupling constant. This approach is equivale nt to the finite-temperature extension of the Beliaev approximation and inc ludes corrections to the Gross-Pitaevskii theory due to both quantum and th ermal fluctuations. For a homogeneous system we explicitly calculate the te mperature dependence of the velocity of propagation and damping rate of zer o sound. In the case of harmonically trapped systems in the thermodynamic l imit, we calculate, as a function of temperature, the frequency shift of th e low-energy compressional and surface modes.