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 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 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 …

Diffusion driven by temperature or concentration gradients is a fundamental mechanism of
energy and mass transport that inherently differs from wave propagation in both physical …

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

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 …

From protein motifs to black holes, topological solitons are pervasive nonlinear excitations
that are robust and can be driven by external fields. So far, existing driving mechanisms all …

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

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 …

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 …