非厄米力学系统基本原理与研究进展

Fundamental principles and research progress of non-Hermitian mechanical systems

非厄米理论是研究开放系统动力学行为的一种理论框架,其概念起源于量子力学,借助该理论可以揭示出奇异点、手性模态转换、拓扑趋肤效应等新奇现象,为反常波动与振动调控提供了新思路.本文着重以力学的语言对非厄米系统的基础概念进行介绍,阐明经典系统与非厄米系统的关联和扩展关系,并介绍相关前沿研究进展.首先介绍非厄米力学系统中的奇异点、宇称-时间反演对称性等基本概念,并介绍奇异点微扰理论及其在高灵敏度传感等领域的应用机理,之后介绍奇异点附近特征值曲面的拓扑结构,以及环绕奇异点的模态演化规律,最后介绍非厄米力学系统中的拓扑波动行为.

Non-Hermitian theory,originated from quantum mechanics,is a theoretical framework for investigating the dynamics of open systems.New phenomena can be revealed with this theory,including exceptional point,chiral mode switching,and topological skin effect,which provide novel concepts for unusual wave and vibration control.This review will provide a comprehensive introduction to basic concepts of non-Hermitian theory in terms of classical mechanical systems,clarify the relationship between classical and non-Hermitian systems,and summarize the cutting-edge research progress in this field.Exceptional points and parity-time symmetry in non-Hermitian systems are firstly introduced.Then,the perturbation theory near exceptional points and its application to enhanced sensitivity are presented.Subsequently,the eigenvalue topological structure near exceptional points and eigenmode evolution in the process of dynamical encircling of exceptional points are discussed.Finally,the topological phase property of non-Hermitian mechanical systems is introduced.