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 …

Non-Hermitian optics is a burgeoning field at the intersection of quantum physics,
electrodynamics, and nanophotonics. It provides a new perspective of the role of gain and …

Nearly one century after the birth of quantum mechanics, parity–time symmetry is
revolutionizing and extending quantum theories to include a unique family of non-Hermitian …

In the past decade, the concept of parity-time $(\mathcal {PT}) $ symmetry, originally
introduced in non-Hermitian extensions of quantum mechanical theories, has come into …

Zero-energy particles (such as Majorana fermions) are newly predicted quasiparticles and
are expected to play an important role in fault-tolerant quantum computation. In conventional …

Recent years have seen a tremendous progress in the theory and experimental
implementations of non-Hermitian photonics, including all-lossy optical systems as well as …

Non-Bloch-band theory describes bulk energy spectra and topological invariants in non-
Hermitian crystals with open boundaries, where the bulk eigenstates are squeezed toward …

Non-Hermitian photonics and topological photonics, as new research fields in optics, have
attracted much attention in recent years, accompanying by a great deal of new physical …

The topological edge state (TES) in a one-dimensional optical lattice has exhibited robust
field localization or waveguiding against the structural perturbations that would give rise to …

Exploring the concept of non-Hermitian Hamiltonians respecting parity-time symmetry with
classical wave systems is of great interest as it enables the experimental investigation of …