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 past decades have witnessed an explosion of interest in topological materials, and a lot
of mathematical concepts have been introduced in condensed matter physics. Among them …

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 …

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 …

Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary
correspondence, including the failure of bulk Bloch band invariants in predicting 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 …

Topological photonics is a rapidly emerging field of research in which geometrical and
topological ideas are exploited to design and control the behavior of light. Drawing …

We study the Hatano-Nelson model, ie, a one-dimensional non-Hermitian chain of spinless
fermions with nearest-neighbor nonreciprocal hop**, in the presence of repulsive nearest …

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 …