任意维中的量子化涡旋和超流：结构、能量学和动力学
Quantized vortices and superflow in arbitrary dimensions: Structure, energetics and dynamics
摘要：
量子化涡旋周围的超流的结构和能量学，以及这些涡旋从该超流继承的运动，在任意维度的氦-4的超流性的一般设置中进行了探索。在三维和四维超流的情况下，涡旋可以被理想化为余维2的物体，例如一维环和二维闭合表面。利用涡旋超流与安培-麦克斯韦静磁学的类比，构造了包含任意指定涡旋集合的平衡超流。的能量的超流被发现采取一个简单的形式是光滑的，渐近大的涡，涡核的大小相比。对涡的运动进行了一般分析，并对超球面涡和弱畸变超平面涡的特殊情况进行了分析。在所有维度中，涡旋运动反映涡旋几何形状。在四维和更高维中，这不仅包括涡旋形状的外在方面，也包括通过经典几何的第一和第二基本形式进入的涡旋形状的内在方面。对于推广了三维超流涡环的超球涡，确定了能量-动量关系。简单的缩放参数恢复这些结果的基本特征，数值和对数因子。
英文摘要：
The structure and energetics of superflow around quantized vortices, and the motion inherited by these vortices from this superflow, are explored in the general setting of the superfluidity of helium-four in arbitrary dimensions. The vortices may be idealized as objects of co-dimension two, such as one-dimensional loops and two-dimensional closed surfaces, respectively, in the cases of three- and four-dimensional superfluidity. By using the analogy between vorticial superflow and Ampere-Maxwell magnetostatics, the equilibrium superflow containing any specified collection of vortices is constructed. The energy of the superflow is found to take on a simple form for vortices that are smooth and asymptotically large, compared with the vortex core size. The motion of vortices is analyzed in general, as well as for the special cases of hyper-spherical and weakly distorted hyper-planar vortices. In all dimensions, vortex motion reflects vortex geometry. In dimension four and higher, this includes not only extrinsic but also intrinsic aspects of the vortex shape, which enter via the first and second fundamental forms of classical geometry. For hyper-spherical vortices, which generalize the vortex rings of three dimensional superfluidity, the energy-momentum relation is determined. Simple scaling arguments recover the essential features of these results, up to numerical and logarithmic factors.
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