Classical and quantum vortex leapfrogging in two-dimensional channels
Classical and quantum vortex leapfrogging in two-dimensional channels
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DOI：
10.1017/jfm.2020.1094
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发表时间：
2020-06
影响因子：
3.7
通讯作者：
L. Galantucci;M. Sciacca;N. Parker;A. Baggaley;C. Barenghi
中科院分区：
文献类型：
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作者：
L. Galantucci;M. Sciacca;N. Parker;A. Baggaley;C. Barenghi
摘要同轴涡旋环的跳越效应是自亥姆霍兹时代以来人们就注意到的一种著名效应。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。这些系统的强约束特性激发了对窄通道内涡跃迁的研究。使用二维点涡模型，我们表明，在二维通道的约束几何中，动力学比在无界域中更丰富：除了已知的标准跨越式和无标准跨越式之外，我们还确定了图像驱动跨越式和周期轨道的新制度。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也存在所有四种状态。最后，我们讨论了经典涡旋和量子涡旋跨越之间的区别，当量子愈合长度与涡旋分离或通道大小相比变得显着时，以及由于高速，冷凝物中的压缩效应变得显着时，就会出现这种差异。
Abstract 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 characterises 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: alongside the known regimes of standard leapfrogging and the absence of it, we identify new regimes of image-driven 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.