Hydrodynamic VS collisionless dynamics of a 1D harmonically trapped Bose gas

Abstract

By using a sum rule approach we investigate the transition between the hydrodynamic and the collisionless regime of the collective modes in a 1D harmonically trapped Bose gas. Both the weakly interacting gas and the Tonks-Girardeau limits are considered. We predict that the excitation of the dipole compression mode is characterized, in the high temperature collisionless regime, by a beating signal of two different frequencies (${\omega }_z$ and $3{\omega }_z$) while, in the high temperature collisional regime, the excitation consists of a single frequency ($\sqrt{7}{\omega }_z$). This behaviour differs from the case of the lowest breathing mode whose excitation consists of a single frequency ($2{\omega }_z$) in both regimes. Our predictions for the dipole compression mode open promising perspectives for the experimental investigation of collisional effects in 1D configurations.

arXiv comment8 pages, 2 figures

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