A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

This review describes the emerging field of waveguide quantum electrodynamics concerned
with the interaction of photons propagating in a waveguide with localized quantum emitters …

Rapidly growing demands for fast information processing have launched a race for creating
compact and highly efficient optical devices that can reliably transmit signals without losses …

Thouless pumping provides one of the simplest manifestations of topology in quantum
systems and has attracted a lot of recent interest, both theoretically and experimentally …

The topological properties of an object, associated with an integer called the topological
invariant, are global features that cannot change continuously but only through abrupt …

Non-Hermiticity significantly enriches the properties of topological models, leading to exotic
features such as the non-Hermitian skin effects and non-Bloch bulk-boundary …

Topological edge modes are excitations that are localized at the materials' edges and yet
are characterized by a topological invariant defined in the bulk. Such bulk–edge …

Topological photonics seeks to control the behaviour of the light through the design of
protected topological modes in photonic structures. While this approach originated from …

There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

The topological phases of matter are characterized using the Berry phase, a geometrical
phase associated with the energy-momentum band structure. The quantization of the Berry …