Damping in 2D and 3D dilute Bose gases

Damping in two-dimensional (2D) and 3D dilute gases is investigated using both the hydrodynamical approach and the Hartree-Fock-Bogoliubov (HFB) approximation. We found that both methods are good for Beliaev damping at zero temperatures and Landau damping at very low temperatures. However, at high temperatures, the hydrodynamical approach overestimates the Landau damping and HFB gives a precise asymptotic behavior. This result shows that the comparison of the theoretical calculation using the hydrodynamical approach and the experimental data for high temperatures by Vincent Liu (1997 Phys. Rev. Lett. 79 4056) is not valid. For 2D systems, we show that the Beliaev damping rate is proportional to k(3) and the Landau damping rate is proportional to T-2 for low temperatures and to T for high temperatures. We also show that in 2D the hydrodynamical approach gives the same result for zero temperature and for low temperature as HFB, but overestimates the Landau damping for high temperatures.