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 …

A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity
to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non …

We establish exact relations between the winding of “energy”(eigenvalue of Hamiltonian) on
the complex plane as momentum traverses the Brillouin zone with periodic boundary …

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 …

The past decades have witnessed the flourishing of non-Hermitian physics in non-
conservative systems, leading to unprecedented phenomena of unidirectional invisibility …

We consider conditions for the existence of boundary modes in non-Hermitian systems with
edges of arbitrary codimension. Through a universal formulation of formation criteria for …

One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect,
namely, that the eigenstates are exponentially localized at the boundary of the system. For …

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

We provide a systematic and self-consistent method to calculate the generalized Brillouin
zone (GBZ) analytically in one-dimensional non-Hermitian systems, which helps us to …