论文标题
纠结的涡流线：量子湍流的动态，几何和拓扑
Tangled vortex lines: dynamics, geometry and topology of quantum turbulence
论文作者
论文摘要
接近绝对零，超流体液氦在宏观长度尺度上显示量子特性。一种特性，超流体，意味着粘度为零的流动。另一个属性是复杂波函数的存在，将旋转限制在薄的离散涡流线上，每个涡流均带有一个量子的循环。因此，如果搅拌液体氦，它会变得湍流，但以一种特殊的方式：它是湍流的状态，该状态由液体中的定量涡流缠绕而没有粘度。令人惊讶的是，这种无序状态（几年前我称为量子湍流）具有许多特性，具有普通的湍流，因为它代表了其必不可少的骨架。这些讲座试图将动力学，几何形状和量子湍流的拓扑联系起来。尽管最近取得了很多进展，但仍然有许多开放问题。这里使用和描述的一些方法（例如，平滑的涡度，交叉数的使用）具有一个范围，显然超出了绝对零接近湍流的引人入胜的问题。
Near absolute zero, superfluid liquid helium displays quantum properties at macroscopic length scales. One property, superfluidity, means flow with zero viscosity. Another property, the existence of a complex wavefunction, constrains the rotation to thin, discrete vortex lines carrying one quantum of circulation each. Therefore, if liquid helium is stirred, it becomes turbulent, but in a peculiar way: it is a state of turbulence consisting of a tangle of quantised vortex lines in a fluid without viscosity. Surprisingly, this disordered state, which I called quantum turbulence years ago, shares many properties with ordinary turbulence as it represents its essential skeleton. These lectures attempt to relate the dynamics, the geometry and the topology of quantum turbulence. Although recently much progress has been made, there are still many open questions. Some of the methods which have been used and are described here (e.g. the smoothed vorticity, the use of crossing numbers) have a scope which clearly goes beyond the fascinating problem of turbulence near absolute zero.
