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

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.