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 …

Exploiting the interplay between gain, loss and the coupling strength between different
optical components creates a variety of new opportunities in photonics to generate, control …

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 …

Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity
occurs, for instance, in active matter,,,,–, non-equilibrium systems,–, networks of neurons …

The bulk-boundary correspondence is among the central issues of non-Hermitian
topological states. We show that a previously overlooked “non-Hermitian skin effect” …

In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry
have attracted considerable attention. In particular, the realization that the interplay between …

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 …

The relation between chiral edge modes and bulk Chern numbers of quantum Hall
insulators is a paradigmatic example of bulk-boundary correspondence. We show that the …

In the past few years, concepts from non-Hermitian (NH) physics, originally developed within
the context of quantum field theories, have been successfully deployed over a wide range of …