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 …

Non-Hermitian theory is a theoretical framework used to describe open systems. It offers a
powerful tool in the characterization of both the intrinsic degrees of freedom of a system and …

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 …

This article reviews recent developments in the non-Hermitian skin effect (NHSE),
particularly on its rich interplay with topology. The review starts off with a pedagogical …

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 …

Skin effect, experimentally discovered in one dimension, describes the physical
phenomenon that on an open chain, an extensive number of eigenstates of a non-Hermitian …

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 …

A non-Hermitian system can exhibit extensive sensitivity of its complex energy spectrum to
the imposed boundary conditions, which is beyond any known phenomenon from Hermitian …

The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin
effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band …