几何诱导的絮凝与无缺陷曲面上的拓扑声
Geometry-induced flocking and topological sound on a defect-free curved surface
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中文总结 AI 辅助
本研究证明在无缺陷的环面上，曲率本身即可通过非厄米Dirac算子产生并保护拓扑声，连接了非厄米拓扑、微分几何与活性物质流体动力学。
中文摘要 AI 辅助
我们研究了环面上的有序极性活性絮凝，并表明拓扑声在无拓扑缺陷或物理边界的紧致弯曲表面上持续存在。利用协变Toner Tu理论，我们推导出一个有效的非厄米Dirac算子，其曲率诱导的质量在外赤道和内赤道之间改变符号，产生两个Jackiw Rebbi畴壁。这些畴壁支持共传播但不同的手性边缘激发：一个定域在正曲率外赤道上的密度模和一个定域在负曲率内赤道上的Goldstone模。体带具有相反的半整数Chern数，其跨越畴壁的跳跃由高斯曲率的符号决定。我们进一步表明，定域模受一维Callias指标定理保护，而局部指标之和在紧致曲面上满足Poincare Hopf定理。我们的结果表明，仅曲率本身，独立于缺陷和边界，就足以在活性物质中产生并保护拓扑声，为非厄米拓扑、微分几何和集体运动流体动力学理论之间提供了统一联系。
英文摘要
We study an ordered polar active flock on a torus and show that topological sound persists on a compact curved surface without topological defects or physical boundaries. Using the covariant Toner Tu theory, we derive an effective nonHermitian Dirac operator whose curvature-induced mass changes sign across the outer and inner equators, producing two Jackiw Rebbi domain walls. These support co-propagating but distinct chiral edge excitations: a density mode localized on the positively curved outer equator and a Goldstone mode localized on the negatively curved inner equator. The bulk bands possess opposite half-integer Chern numbers whose jumps across the domain walls are determined by the sign of the Gaussian curvature. We further show that the localised modes are protected by a one-dimensional Callias index theorem, while the sum of the local indices obeys the Poincare Hopf theorem on the compact surface. Our results establish that curvature alone, independent of defects and boundaries, is sufficient to generate and protect topological sound in active matter, providing a unified connection between non-Hermitian topology, differential geometry, and hydrodynamic theory of collective motion.
发表机构
- National Institute of Technology Karnataka（卡纳塔克国立理工学院）
- DIT University（迪特大学）
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