玻色-爱因斯坦凝聚体通过可穿透势垒的跨临界流动
Transcritical flow of a Bose-Einstein condensate through a penetrable barrier
摘要：
本文利用一维Gross-Pitaevskii方程的局部“水力”解和描述色散激波对上下游间断的分解的Whitham调制方程的解，分析研究了玻色-爱因斯坦凝聚体通过宽排斥可穿透壁的跨临界流动问题。结果表明，在物理上合理的参数范围内，下游色散激波附着在势垒上，有效地代表了实验中可以观察到的非常慢的暗孤子的训练。孤子发射速率、训练中孤子的振幅和拖曳力由BEC来流速度和势垒强度决定。一个很好的协议与直接数值解的证明。讨论了与最近实验的联系。
英文摘要：
The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the localized "hydraulic" solution of the 1D Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train and the drag force are determined in terms of the BEC oncoming flow velocity and the strength of the potential barrier. A good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.
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