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Conclusions

We have studied motion of an impurity through the condensate at zero temperature by considering the perturbation of a stationary solution of the GP equation. We calculated the induced mass which contributes to the mass of normal component. We find that the motion at small velocities is dissipationless in one-, two-, and three- dimensional systems, although movement with velocities larger than the speed of sound leads to a non-zero drag force due to Cherenkov radiation of phonons. The expressions for the drag force are calculated. We used results for the dynamic form factor of exact Lieb-Liniger theory to investigate the velocity dependence of the drag force in a 1D system. The form factor was calculated with the help of the Haldane method of calculations of correlation functions. The drag force exists at an arbitrarily small velocity of motion, but is very small in the mean-field limit. The dynamic form-factor can be also directly measured by applying a harmonic time-dependent perturbation on one-dimensional condensates [GVL+01,SMS+04].


next up previous contents
Next: Interacting fermions in highly Up: Motion of a heavy Previous: One-dimensional system. Bethe-ansatz theory   Contents
G.E. Astrakharchik 15-th of December 2004