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arXiv:0705.3180 · Journal of Experimental and Theoretical Physics

Generation of linear waves in Bose-Einstein condensate flow past an obstacle

Yu. G. Gladush, A. M. Kamchatnov

Published Oct 1, 2007• 12 citations
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Abstract

A theory of linear wave patterns developing in Bose-Einstein condensate flow past an obstacle is developed. The results obtained characterize the wave crestline geometry and the far-field dependence of the wave amplitude on coordinates. The theoretical predictions agree with the results of previous numerical simulations and provide a qualitative explanation of experiments on the flow of a Bose-Einstein condensate released from a trap past an obstacle.

DOI
10.1134/s1063776107090075

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A theory of linear wave patterns developing in Bose-Einstein condensate flow past an obstacle is developed. The results obtained characterize the wave crestline geometry and the far-field dependence of the wave amplitude on coordinates. The theoretical predictions agree with the results of previous numerical simulations and provide a qualitative explanation of experiments on the flow of a Bose-Einstein condensate released from a trap past an obstacle.
The theory of stationary linear wave patterns generated in a supersonic flow of a Bose–Einstein condensate past a point-like obstacle is developed. It is shown that they are located mainly outside the Mach cone corresponding to infinitely long wavelengths. The shape of wave crests and dependence of amplitude on coordinates far enough from the obstacle are calculated. The results are in good agreement with the results of numerical simulations. The theory gives a qualitative description of experiments with Bose–Einstein condensate flow past an obstacle after the condensate's release from a trap.
We investigate by numerical simulations the pattern formation after an oscillating attractive-repulsive obstacle inserted into the flow of a Bose-Einstein condensate. For slow oscillations we observe a complex emission of vortex dipoles. For moderate oscillations organized lined up vortex dipoles are emitted. For high frequencies no dipoles are observed but only lined up dark fragments. The results shows that the drag force turns negative for sufficiently high frequency. We also successfully model the ship waves in front of the obstacle. In the limit of very fast oscillations all the excitations of the system tend to vanish.
The stability of dark solitons generated by supersonic flow of a Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to the decay of disturbances of solitons at a fixed distance from the obstacle and the formation of effectively stable dark solitons. This phenomenon explains the surprising stability of the flow picture that has been observed in numerical simulations.