Fundamental principles and research progress of non-Hermitian mechanical systems

GENG Linlin; YUAN Jinbo; CHENG Wen; HU Gengkai; ZHOU Xiaoming

doi:10.6052/1000-0992-23-034

Volume 54 Issue 1

Mar. 2024

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Geng L L, Yuan J B, Cheng W, Hu G K, Zhou X M. Fundamental principles and research progress of non-Hermitian mechanical systems. Advances in Mechanics, 2024, 54(1): 1-60 doi: 10.6052/1000-0992-23-034

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Geng L L, Yuan J B, Cheng W, Hu G K, Zhou X M. Fundamental principles and research progress of non-Hermitian mechanical systems. Advances in Mechanics, 2024, 54(1): 1-60 doi: 10.6052/1000-0992-23-034

Geng L L, Yuan J B, Cheng W, Hu G K, Zhou X M. Fundamental principles and research progress of non-Hermitian mechanical systems. Advances in Mechanics, 2024, 54(1): 1-60 doi: 10.6052/1000-0992-23-034

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Fundamental principles and research progress of non-Hermitian mechanical systems

doi: 10.6052/1000-0992-23-034

Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

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Corresponding author: zhxming@bit.edu.cn
Received Date: 2023-09-11
Accepted Date: 2023-12-27

Available Online: 2024-01-09

Publish Date: 2024-03-24

Abstract

Abstract

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.
- non-Hermitian system,
- non-conservative system,
- exceptional point,
- parity-time symmetry,
- non-Hermitian topology

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