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 …

BACKGROUND Singularities are critical points for which the behavior of a mathematical
model governing a physical system is of a fundamentally different nature compared to the …

The development of new artificial structures and materials is today one of the major research
challenges in optics. In most studies so far, the design of such structures has been based on …

Both theoretical and experimental studies of topological phases in non-Hermitian systems
have made a remarkable progress in the last few years of research. In this article, we review …

This report on progress explores recent advances in our theoretical and experimental
understanding of the physics of open quantum systems (OQSs). The study of such systems …

The notion of non-Hermitian optics and photonics rooted in quantum mechanics and
photonic systems has recently attracted considerable attention ushering in tremendous …

The appearance of so-called exceptional points in the complex spectra of non-Hermitian
systems is often associated with phenomena that contradict our physical intuition. One …

Utilizing exact diagonalization techniques, we investigate a one-dimensional, nonreciprocal,
interacting hard-core boson model under a Stark potential with tail curvature. By employing …

For a general complex scattering potential defined on a real line, we show that the equations
governing invisibility of the potential are invariant under the combined action of parity and …

Non-Hermitian systems host unconventional physical effects that be used to design new
optical devices. We study a non-Hermitian system consisting of 1D planar optical …