Damping in 2D and 3D dilute Bose gases

TL;DR

This paper compares hydrodynamical and Hartree-Fock-Bogoliubov methods for damping in 2D and 3D dilute Bose gases, highlighting their accuracy at different temperatures and providing specific damping rate dependencies.

Contribution

It demonstrates the conditions under which each theoretical approach accurately predicts damping rates in dilute Bose gases, especially at varying temperatures.

Findings

Both methods accurately predict Beliaev damping at zero temperature.

Hydrodynamical approach overestimates Landau damping at high temperature.

In 2D, damping rates depend on temperature and wavevector as specified.

Abstract

Damping in 2D and 3D dilute gases is investigated using both the hydrodynamical approach and the Hartree-Fock-Bogoliubov (HFB) approximation . We found that the both methods are good for the Beliaev damping at zero temperature and Landau damping at very low temperature, however, at high temperature, the hydrodynamical approach overestimates the Landau damping and the HFB gives a better approximation. This result shows that the comparison of the theoretical calculation using the hydrodynamical approach and the experimental data for high temperature done by Vincent Liu (PRL {\bf21} 4056 (1997)) is not proper. For two-dimensional 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 temperature and to $T$ for high temperature. We also show that in two dimensions the hydrodynamical approach gives the same result for zero temperature and for low temperature as HFB, but overestimates the Landau damping for high temperature.