Abstract

By using the time-dependent mean-field approach based on the Popov approximation, the Landau damping in a Bose-Fermi superfluid mixture in the presence of a long-range \( 1/r\) interaction between bosons at finite temperature is studied. For a homogeneous three-dimension (3D) gas, we will show, since both Bose-Fermi and the \( 1/r\) interactions contributions are exponentially suppressed, the contact interaction has the dominant role to the low-temperature behavior of the Landau damping and the temperature behavior of the damping rate due to the \( 1/r\) and Bose-Fermi interactions similar to contact interaction is linear at high temperatures. In a two-dimension (2D) system, we will also show that the damping rate in a gas with the \( 1/r\) interaction has a minor role in comparison with contact and dipole-dipole interactions at all ranges of temperatures, and the low-temperatures behavior of the damping rate due to both the \( 1/r\) and dipole-dipole interactions scales as \( e^{-1/T}\) while the contact contribution changes as \(T^{2}\) . Our results have important consequences for ongoing experiments and theoretical researches on ultracold gases with repulsive or attractive long-range \( 1/r\) interaction.

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