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arXiv:hep-lat/0010054 · Nuclear Physics B - Proceedings Supplements

Damping and the Hartree ensemble approximation

M. Sallé, Jan Smit A, Jeroen C. Vink

Published Mar 1, 2001• 3 citations
arXivHTMLPDF
DOI
10.1016/s0920-5632(01)00995-1

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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.
The monopole and quadrupole oscillations of a Bose-Einstein condensate (BEC) gas trapped in a spherically symmetric potential are calculated using the time-dependent Hartree approximation which enables us to use an orthonormal single-particle basis for the description of both the condensate and noncondensate components. It is found that the monopole mode has a much smaller damping rate than the quadrupole mode. The obtained temperature dependence of the frequency shifts and the damping rates of the collective oscillations are found to be consistent with experimental data obtained for BEC gases in anisotropic trapping potentials. A comparison between the time-dependent Hartree approximation and the time-dependent Hartree-Fock approximation is also made and it is found that there is a rather small difference.