Motivated by ongoing experimental efforts to make closed Bose-Einstein condensate shells in microgravity environments, this work studies the energy and dynamics of singly quantized vortices on a thin spherical superfluid shell, where the overall vortex charge must vanish (as on any compact surface). For each vortex, stereographic projection yields the corresponding complex potential on the tangent plane. The resulting stream function then provides both the total energy and the dynamics of a system of overall neutral vortices on a spherical film. Although a single-vortex dipole follows a simple dynamical orbit, four vortices can present a variety of situations. We study a few symmetric initial configurations and then focus on the special case of two small vortex dipoles.

中文翻译：

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球形薄膜上的超流体涡旋动力学

受正在进行的实验努力的推动，以在微重力环境中制造封闭的玻色-爱因斯坦冷凝壳，这项工作研究了球形超流体薄壳上单个量化涡流的能量和动力学，在该壳中，总涡流必须消失（在任何紧凑的表面上）。对于每个涡旋，立体投影都会在切线平面上产生相应的复数电势。然后，所得的流函数既提供了总能量，又提供了球形薄膜上的整体中性涡流系统的动力学。尽管单涡旋偶极子遵循简单的动力学轨道，但四个涡旋可呈现多种情况。我们研究了一些对称的初始配置，然后重点研究了两个小涡旋偶极子的特殊情况。