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 …

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 …

Recent progress on nonlinear properties of parity-time (PT)-symmetric systems is
comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum …

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 …

The bulk-boundary correspondence is crucial to topological insulators. It associates the
existence of boundary states (with zero energy and possessing chiral or helical properties) …

One of the most widely known building blocks of modern physics is Heisenberg's
indeterminacy principle. Among the different statements of this fundamental property of the …

The visualization of an exceptional point in a PT-symmetric directional coupler (DC) is
demonstrated. In such a system the exceptional point can be probed by varying only a single …

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define
a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We …

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 …

We present a survey of some recent theoretical and experimental studies on nonlinear
waves that form and propagate in a broad class of optical and matterwave media. The article …