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 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 …

The study of the laws of nature has traditionally been pursued in the limit of isolated systems,
where energy is conserved. This is not always a valid approximation, however, as the …

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 …

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 …

There are two prominent applications of the mathematical concept of topology to the physics
of materials: band topology, which classifies different topological insulators and semimetals …

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 …