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 …

Recent years have seen remarkable development in open quantum systems effectively
described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological …

After many years of development of the basic tools, quantum simulation with ultracold atoms
has now reached the level of maturity at which it can be used to investigate complex …

In spatially periodic Hermitian systems, such as electronic systems in crystals, the band
structure is described by the band theory in terms of the Bloch wave functions, which …

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” …

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in
controlling dissipation have brought about unprecedented flexibility in engineering non …

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 …

A d-dimensional second-order topological insulator (SOTI) can host topologically protected
(d-2)-dimensional gapless boundary modes. Here, we show that a 2D non-Hermitian SOTI …