标题： 二维$p$-atics 中通过周期边界缺陷相互作用 显示英文标题

标题： Defect Interactions Through Periodic Boundaries in Two-Dimensional $p$-atics

摘要： 周期性边界条件是一种常用的工具，用于有效地模拟无限域。 然而，二维周期性域在拓扑上与无限平面不同，这引发了这样一个问题：周期性边界条件如何影响本身具有拓扑性质的系统？ 在本工作中， 我推导出二维$p$-atic液晶的取向场的解析表达式，这些系统具有$p$-重旋转对称性，在受二维周期性边界条件约束的平面上存在拓扑缺陷。 我展示了这种取向场会导致缺陷之间出现异常的相互作用，这种相互作用偏离了通常的库仑相互作用，这一结论通过向列液晶（$p = 2$）的连续体模拟得到了验证。 这种相互作用被理解为由指向场中的非奇异拓扑孤子介导的，这些孤子由周期性边界条件稳定。 结果表明，在分析拓扑缺陷之间的相互作用时，考虑域的拓扑结构而不是仅仅几何结构是重要的。 显示英文摘要

摘要： Periodic boundary conditions are a common tool used to emulate effectively infinite domains. However, two-dimensional periodic domains are topologically distinct from the infinite plane, eliciting the question: How do periodic boundaries affect systems with topological properties themselves? In this work, I derive an analytical expression for the orientation fields of two-dimensional $p$-atic liquid crystals, systems with $p$-fold rotational symmetry, with topological defects in a flat domain subject to periodic boundary conditions in two-dimensions. I show that this orientation field leads to an anomalous interaction between defects that deviates from the usual Coulomb interaction, which is confirmed through continuum simulations of nematic liquid crystals ($p = 2$). The interaction is understood as being mediated by non-singular topological solitons in the director field which are stabilized by the periodic boundary conditions. The results show the importance of considering domain topology, not only geometry, when analyzing interactions between topological defects.