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 …

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 non-Hermitian skin effect (NHSE), the accumulation of eigen–wave functions at
boundaries of open systems, underlies a variety of exotic properties that defy conventional …

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

Topological modes (TMs) are usually localized at defects or boundaries of a much larger
topological lattice,. Recent studies of non-Hermitian band theories unveiled the non …

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

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 …

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 …