Topology and symmetry have emerged as compelling guiding principles to predict and harness the propagation of waves in natural and artificial materials. Be it for quantum particles (such as electrons) or classical waves (such as light, sound or mechanical motion), these concepts have so far been mostly developed in idealized scenarios, in which the wave amplitude is neither attenuated nor amplified, and time evolution is unitary. In recent years, however, there has been a considerable push to explore the consequences of topology and symmetries in non-conservative, non-equilibrium or non-Hermitian systems. A plethora of driven artificial materials has been reported, blurring the lines between a wide variety of fields in physics and engineering, including condensed matter, photonics, phononics, optomechanics, as well as electromagnetic and mechanical metamaterials. Here we discuss the latest advances, emerging opportunities and open challenges for combining these exciting research endeavours into the new pluridisciplinary field of non-Hermitian topological systems.

拓扑和对称性已成为令人信服的指导原则，可以预测和利用自然和人造材料中的波传播。到目前为止，无论是用于量子粒子（例如电子）还是经典波（例如光，声音或机械运动），这些概念大多是在理想的情况下开发的，在理想情况下，波的振幅既不衰减也不放大，并且随时间而变化。是单一的。但是，近年来，人们大力推动了拓扑结构和对称性在非保守，非平衡或非Hermitian系统中的后果。据报道，有大量人造材料被驱使，从而模糊了物理学和工程学各个领域之间的界线，包括凝结物质，光子学，声子学，光力学，以及电磁和机械超材料。在这里，我们讨论了将这些激动人心的研究成果结合到非Hermitian拓扑系统的新的多学科领域中的最新进展，新兴机遇和挑战。