Mermin-Ho 涡旋

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定义 · 4.10 超流体 ${}^3\mathrm{He}-\mathrm{A}$ 中的织构

${\mathbb{Z}}_2$ 的一个显著性质是加法 $1+1=0$：两个向错合并会产生一个平庸织构。通过合并两个向错，我们可以构造出一种看起来像双涡量涡旋（同伦类“2”）却没有奇异核的织构；参见图 4.31(a)。容易验证，回路 $\alpha$ 的像绕 $\mathbb{R}{P}^3$ 两圈，而较小回路 $\beta$ 的像则可收缩为一点。这种织构称为 Anderson-Toulouse 涡旋(Anderson-Toulouse vortex)（Anderson and Toulouse 1977）。Mermin 与 Ho (1976) 指出，若介质处于圆柱形容器中，边界会施加条件 $\hat{l}\perp$（边界），于是涡旋在表面处被截断，参见图 4.31(b)（即 Mermin-Ho 涡旋(Mermin-Ho vortex)）。

英文原文

A remarkable property of ${\mathbb{Z}}_2$ is the addition $1+1=0$ ; the coalescence of two disgyrations produces a trivial texture. By merging two disgyrations, we may construct a texture that looks like a vortex of double vorticity (homotopy class ‘2’) without a singular core; see figure 4.31(a). It is easy to verify that the image of the loop $\alpha$ traverses $\mathbb{R}{P}^3$ twice while that of the smaller loop $\beta$ may be shrunk to a point. This texture is called the Anderson-Toulouse vortex (Anderson and Toulouse 1977). Mermin and Ho (1976) pointed out that if the medium is in a cylinder, the boundary imposes the condition $\hat{l}\perp$ (boundary) and the vortex is cut at the surface, see figure 4.31(b) (the Mermin-Ho vortex).

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