论文标题
非热拓扑和特殊的几何形状
Non-Hermitian Topology and Exceptional-Point Geometries
论文作者
论文摘要
非热理论是一个理论框架，在描述开放系统方面表现出色。它为系统的内在自由度（DOF）和与外部环境的相互作用的表征提供了强大的工具。非热框架由数学结构组成，这些结构与赫尔米尔人的理论根本不同。这些结构不仅是精确调整用于应用的非铁质系统的新颖方法，还引起了Hermitian系统中未发现的拓扑结构。在本文中，我们通过建立与复杂特征值和生物双歧型特征向量的行为建立关系来全面回顾非高级拓扑。特别注意特殊点 - 具有非平凡拓扑特性的复杂特征值歧管上的分支点奇异性。我们还讨论了非热带乐队拓扑的最新发展，例如非铁皮皮肤效应和非铁质拓扑分类
Non-Hermitian theory is a theoretical framework that excels at describing open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external environment. The non-Hermitian framework consists of mathematical structures that are fundamentally different from those of Hermitian theories. These structures not only underpin novel approaches for precisely tailoring non-Hermitian systems for applications but also give rise to topologies not found in Hermitian systems. In this paper, we comprehensively review non-Hermitian topology by establishing its relationship with the behaviors of complex eigenvalues and biorthogonal eigenvectors. Special attentions are given to exceptional points - branch-point singularities on the complex eigenvalue manifolds that exhibit non-trivial topological properties. We also discuss recent developments in non-Hermitian band topology, such as the non-Hermitian skin effect and non-Hermitian topological classifications
