二维通道中的经典和量子涡旋蛙跳
Classical and quantum vortex leapfrogging in two-dimensional channels
摘要：
同轴涡环的蛙跳效应是自亥姆霍兹以来就被人们所注意到的一个著名现象。超冷原子气体的最新进展表明，现在可以在量子流体中研究这种效应。强约束的特点，这些系统激发了研究蛙跳的涡在狭窄的渠道。使用二维点涡模型，我们表明，在约束的几何形状的二维通道的动态是丰富的比在一个无界域：alongsize的标准蛙跳和没有它的已知制度，我们确定新的制度向后蛙跳和周期轨道。此外，通过求解玻色-爱因斯坦凝聚体的Gross-Pitaevskii方程，我们证明了量子涡旋的四个区域都存在。最后，我们讨论了经典和量子涡旋蛙跳之间的差异时出现的量子愈合长度变得显着相比，涡旋分离或通道的大小，当，由于高速度，压缩性的影响在冷凝物变得显着。
英文摘要：
The leapfrogging of coaxial vortex rings is a famous effect which has been noticed since the times of Helmholtz. Recent advances in ultra-cold atomic gases show that the effect can now be studied in quantum fluids. The strong confinement which characterizes these systems motivates the study of leapfrogging of vortices within narrow channels. Using the two-dimensional point vortex model, we show that in the constrained geometry of a two-dimensional channel the dynamics is richer than in an unbounded domain: alongsize the known regimes of standard leapfrogging and the absence of it, we identify new regimes of backward leapfrogging and periodic orbits. Moreover, by solving the Gross-Pitaevskii equation for a Bose-Einstein condensate, we show that all four regimes exist for quantum vortices too. Finally, we discuss the differences between classical and quantum vortex leapfrogging which appear when the quantum healing length becomes significant compared to the vortex separation or the channel size, and when, due to high velocity, compressibility effects in the condensate becomes significant.
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