论文标题
$^3 $ He的弦单孔，弦墙，涡流 - 千里和纽约物体
String monopoles, string walls, vortex-skyrmions and nexus objects in polar distorted B-phase of $^3$He
论文作者
论文摘要
可以在早期宇宙的相过渡期间产生复合宇宙学对象 - 千层次 - KLS-SHAFI（KLS）壁，该壁构成了弦和宇宙字符串。超流体$^3 $的最新实验他重现了KLS域墙的形成，该壁为具有不同特征长度的人类控制系统中这些对象的详细研究打开了新领域。这些复合缺陷由两个连续的对称断裂相变形成。在第一个过渡中，琴弦形成，然后在第二个过渡中，字符串变成KLS壁的终止线。以相同的方式，在第一个过渡单孔中形成，然后在第二个过渡中，这些单孔成为字符串的终止点。在这里，我们表明，在第二个过渡的附近，复合缺陷可以由相对同拷贝组描述。这是因为涉及两个分开的长度尺度，这产生了两个不同类别的简并真空状态，$ r_1 $和$ r_2 $，而复合对象则对应于组$π_n（R_1，R_2）$的非平凡元素。我们以所谓的极性扭曲B相的示例讨论了这一点，该相位是在液体扭曲的液体$^3 $中形成的。在此系统中，字符串monopoles终止具有缠绕数的自旋涡旋，而KLS弦墙终止于半量子涡流。在存在磁场的情况下，形成了涡流 - 千里，并将弦单极转换为Nexus。我们还讨论了这些物体的整数值拓扑不变。我们的考虑可以应用于其他冷凝物和宇宙学系统中的复合缺陷。
The composite cosmological objects -- Kibble-Lazarides-Shafi (KLS) walls bounded by strings and cosmic strings terminated by Nambu monopoles -- could be produced during the phase transitions in the early Universe. Recent experiments in superfluid $^3$He reproduced the formation of the KLS domain walls, which opened the new arena for the detailed study of those objects in human controlled system with different characteristic lengths. These composite defects are formed by two successive symmetry breaking phase transitions. In the first transition the strings are formed, then in the second transition the string becomes the termination line of the KLS wall. In the same manner, in the first transition monopoles are formed, and then in the second transition these monopoles become the termination points of strings. Here we show that in the vicinity of the second transition the composite defects can be described by relative homotopy groups. This is because there are two well separated length scales involved, which give rise to two different classes of the degenerate vacuum states, $R_1$ and $R_2$, and the composite objects correspond to the nontrivial elements of the group $π_n(R_1,R_2)$. We discuss this on example of the so-called polar distorted B phase, which is formed in the two-step phase transition in liquid $^3$He distorted by aerogel. In this system the string monopoles terminate spin vortices with even winding number, while KLS string walls terminate on half quantum vortices. In the presence of magnetic field, vortex-skyrmions are formed, and the string monopole transforms to the nexus. We also discuss the integer-valued topological invariants of those objects. Our consideration can be applied to the composite defects in other condensed matter and cosmological systems.
