论文标题
拓扑保护的涡旋结和链接
Topologically protected vortex knots and links
论文作者
论文摘要
我们提出了一类纠结的涡旋结构，这些结构与非亚伯拓扑涡流有关，这些结构可以通过系统允许的局部重新连接和链横梁进行腐烂。我们将这种结构称为拓扑保护。然后，我们将注意力转向由Quaternion Group $ Q_8 $（$ Q_8 $ - 颜色的链接）分类的拓扑涡流，这些链接在组成的系统中可以实现，或者是双轴nematic或Spin-2 Bose-bose-indemstein-rosinstein凝聚力的环状阶段，或者是双轴液体液体晶体和promologed $ qupoliced $ qupolic of topologed $ q的$ nmocogy of tuplocy of tuplocy of tuplice $ q。值得注意的是，我们构建的最强大的不变性，即$ q $ q_8 $颜色的链接的$ q $ - invariant，可用于对$ q_8 $颜色的链接进行分类，以便在涡旋核心上允许本地手术。
We propose a class of tangled vortex structures, tied from non-Abelian topological vortices, which are immune against decaying through local reconnections and strand crossings that are allowed by the system. We refer to such structures as being topologically protected. We then turn our attention to topological vortices classified by the quaternion group $Q_8$ ($Q_8$-colored links), which are realizable in systems consisting either of the biaxial nematic or the cyclic phase of a spin-2 Bose--Einstein condensate, or of biaxial nematic liquid crystal, and prove the existence of topologically protected $Q_8$-colored links. Remarkably, the strongest invariant we construct, the $Q$-invariant of $Q_8$-colored links, can be used to classify $Q_8$-colored links up to allowed local surgeries on the vortex cores.
