拓扑缺陷核心的普适指纹
Universal fingerprint of topological defect cores
- Liaoning Key Laboratory of Cosmology and Astrophysics, College of Sciences, Northeastern University（东北大学理学院）
- Center for Gravitation and Astrophysics, Kunming University of Science and Technology（昆明理工大学引力与天体物理中心）
- Center for Theoretical Physics , Hainan University（海南大学理论物理中心）
- MOE Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University（东北大学教育部智能工业数据分析与优化重点实验室）
- National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University（东北大学国家工业智能与系统优化前沿科学中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究发现拓扑缺陷核心的普适标度律，解析证明其指数源于缺陷核心的V形尖点，经多类数值模拟验证，为拓扑缺陷研究提供新探测手段。
AI中文摘要：
拓扑缺陷在物理学中普遍存在，从凝聚态物理到早期宇宙均有出现。尽管已存在诸多关于拓扑缺陷间关联的普适标度律（如Porod标度），但拓扑缺陷核心的指纹仍在很大程度上未被探索。本文在$k>1/\xi$区域（其中$\xi$为拓扑缺陷的愈合长度）发现了一种普适标度律，其形式为形状因子$S_f \propto k^{-(d+p+2)}$，其中$d$为空间维度，$p$为缺陷余维数。我们通过解析证明，该指数源于缺陷核心处的普适V形尖点，且与底层系统及动力学无关。数值模拟在四种典型框架中验证了该标度律：弱耦合区域的含时Ginzburg-Landau方程和Gross-Pitaevskii方程、强耦合区域的规范/引力对偶模型，以及宇宙学中Friedmann-Robertson-Walker背景下的Klein-Gordon方程。我们的工作为研究从超导体到宇宙学相变等系统中的拓扑缺陷提供了一种新的探测手段。
英文摘要：
Topological defects are ubiquitous in physics, arising from condensed matter physics to the early universe. Although there exist many universal scaling laws for correlations between topological defects, such as Porod scaling, the fingerprint of topological defect cores has remained largely unexplored. Here, we discover a universal scaling law in the region $k>1/ξ$, where $ξ$ is the healing length of the topological defects, taking the scaling of the form factor $S_f \propto k^{-(d+p+2)}$, where $d$ is the spatial dimension and $p$ is the defect codimension. We analytically prove that this exponent originates from a universal V-shaped cusp at the defect core and is independent of the underlying system and dynamics. Numerical simulations verify this scaling law in four typical frameworks: the time-dependent Ginzburg-Landau and Gross-Pitaevskii equations in the weak-coupling regime, the gauge/gravity duality model in the strong-coupling regime, and the Klein-Gordon equation in the Friedmann-Robertson-Walker background in cosmology. Our work provides a new probe for studying topological defects in systems ranging from superconductors to cosmological phase transitions.
