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 …

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-
reaching physical consequences observable in a range of dissipative settings are reviewed …

Bulk–boundary correspondence, a guiding principle in topological matter, relates robust
edge states to bulk topological invariants. Its validity, however, has so far been established …

Quantum random walk is the quantum counterpart of a classical random walk. The classical
random walk concept has long been used as a computational framework for designing …

Non-Hermiticity enriches topological phases beyond the existing Hermitian framework.
Whereas their unusual features with no Hermitian counterparts were extensively explored, a …

We experimentally simulate nonunitary quantum dynamics using a single-photon
interferometric network and study the information flow between a parity-time-(PT-) symmetric …

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

We study entanglement properties of free-fermion systems without Hermiticity by use of
correlation matrix and overlap matrix in the biorthogonal basis. We find at a critical point in …

Despite a long history of studies, acoustic waves are generally regarded as spinless scalar
waves, until recent research revealed their rich structures. Here, we report the experimental …

Yang-Lee edge singularities (YLES) are the edges of the partition function zeros of an
interacting spin model in the space of complex control parameters. They play an important …