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 systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass-spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.

A new type of metamaterial element is proposed to possess time-dependent effective inertial mass, and proved to be valid for the design of the space-time lattice metamaterial that enables non-reciprocal wave propagation. The cell structure is a three-body dynamic system, consisting of a primary body plus two additional bodies that move along the circular orbit. The translational momentum contributed by the orbiting bodies varies periodically depending on their temporal phases, accounting for the time-driven inertial mass observed macroscopically, as verified by the rigorous theoretical derivation. Based on the time-varying mass element, we present the design of the lattice metamaterials with inertial mass that varies periodically in both space and time. Non-reciprocal wave phenomena due to the wave-like modulation of mass are demonstrated by use of the Bloch-based method and the effective-mass representation. The influence of the modulating frequency and amplitude on the asymmetric bandgap is analyzed. The proposed time-varying metamaterial with the non-reciprocal wave behavior is expected to open a new avenue towards unprecedented control over waves and vibrations. (C) 2018 Elsevier Ltd. All rights reserved.

Modern technological advances allow for the study of systems with additional synthetic dimensions. Higher-order topological insulators in topological states of matters have been pursued in lower physical dimensions by exploiting synthetic dimensions with phase transitions. While synthetic dimensions can be rendered in the photonics and cold atomic gases, little to no work has been succeeded in acoustics because acoustic wave-guides cannot be weakly coupled in a continuous fashion. Here, we formulate the theoretical principles and manufacture acoustic crystals composed of arrays of acoustic cavities strongly coupled through modulated channels to evidence one-dimensional (1D) and two-dimensional (2D) dynamic topological pumpings. In particular, the higher-order topological edge-bulk-edge and corner-bulk-corner transport are physically illustrated in finite-sized acoustic structures. We delineate the generated 2D and four-dimensional (4D) quantum Hall effects by calculating first and second Chern numbers and physically demonstrate robustness against the geometrical imperfections. Synthetic dimensions could provide a powerful way for acoustic topological wave steering and open up a platform to explore any continuous orbit in higher-order topological matter in dimensions four and higher. The authors create synthetic dimensions in acoustic crystals composed of cavity arrays, strongly coupled through modulated channels. They provide evidence for 1D and 2D dynamic topological pumping, and show that the higher-order topological sound transport is robust against the geometrical imperfections.

Knots and links have been conjectured to play a fundamental role in a wide range of scientific fields. Recently, tying isolated vortex knots in the complex optical field has been realized. However, how to construct the acoustic vortex knot is still an unknown problem. Here we propose theoretically and demonstrate experimentally the creation of acoustic vortex knots using metamaterials, with decoupled modulation of transmitted phase and amplitude. Based on the numerical simulation, we find that the knot function can be embedded into the acoustic field by designed metamaterials with only 24x24 pixels. Furthermore, using the optimized metamaterials, the acoustic fields with Hopf link and trefoil knot vortex lines have been observed experimentally. Although knots in complex optical fields have been realized experimentally, the realization of acoustic vortex knots is still problematic. Here, the authors have demonstrated the creation of acoustic vortex knots by embedding the knot function into a propagating acoustic field using a metasurface hologram.

The homogenized medium of the gyro lattice with the mechanical quantum Hall effect, here denoted as the gyroscopic elastic medium, is governed by a new set of elastodynamic equations with the chiral density. This paper presents a generic theory based on the Stroh formalism to disclose the non-reciprocal Rayleigh waves supported by the gyroscopic medium. The Stroh formulation is investigated in the general case of anisotropic elasticity, and after introducing the chiral density, it is extended to yield new forms of eigenvalue equations, which are distinct for surface waves traveling in opposite directions. Numerical examples are performed in the isotropic elasticity scheme, illustrating the non-reciprocal Rayleigh waves as well as the evolution of the particle motion trajectory and polarization at shallow depths as the gyro coupling magnitude increases. The developed theory confirms the prediction for the classical Rayleigh wave that is reciprocal when the gyro coupling term vanishes. Finally, a general effective-medium method that relies on the surface response to external excitation is proposed for the estimation of the overall properties of gyroscopic composite materials in the long-wavelength regime. Consistency in the wave response of gyroscopic composites with periodic inclusions and their effectively homogeneous materials is demonstrated for a large range of gyro coupling constants. (C) 2020 Elsevier Ltd. All rights reserved.