Abstract
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 k3 and the Landau damping rate is proportional to T2 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.
Highlights
The experimental realization of Bose-Einstein condensation (BEC) in magnetically trapped akali atoms [1, 2, 3] provides a good tool to study the properties of 3D dilute Bose gases
For the high temperature, Liu showed higher Landau damping rate than those obtained by Szepfalusy and Kondor, while the hign-temperature behavior could be reproduced by Pitaevskii and Stringari
We show that the hydrodynamical approach overestimates the damping rate at high temperatures, both for 3D and 2D systems and we calculate the Balieav and Landau damping rates for a 2D uniform Bose gas using the semi-classical Hartree-FockBogoliubov (HFB) approach
Summary
The experimental realization of Bose-Einstein condensation (BEC) in magnetically trapped akali atoms [1, 2, 3] provides a good tool to study the properties of 3D dilute Bose gases. Pitaevskii and Stringari [12] investigated Landau damping in a weakly interacting uniform as well as non-uniform Bose gas by means of semi-classical theory. They showed that for the uniform Bose gas, it reproduces known results for both the low temperature asymptotic behaviour of the phonon coupling. We show that the hydrodynamical approach overestimates the damping rate at high temperatures, both for 3D and 2D systems and we calculate the Balieav and Landau damping rates for a 2D uniform Bose gas using the semi-classical Hartree-FockBogoliubov (HFB) approach. IV the HFB approximation is developed to calculate 3D and 2D Beliaev and Landau damping
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