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 …

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 …

In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry
have attracted considerable attention. In particular, the realization that the interplay between …

In the past few years, concepts from non-Hermitian (NH) physics, originally developed within
the context of quantum field theories, have been successfully deployed over a wide range of …

This chapter introduces the basic ideas of P T-symmetric systems. It begins with a brief
discussion of closed (isolated) and open (non-isolated) systems and explains that P T …

We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac
equation. Such modes appear at interfaces between media with different “masses” and/or …

The ability to control the modes oscillating within a laser resonator is of fundamental
importance. In general, the presence of competing modes can be detrimental to beam …

An all-Si photonic structure emulating the quantum-valley-Hall effect is proposed. We show
that it acts as a photonic topological insulator (PTI), and that an interface between two such …

The Dirac cone underlies many unique electronic properties of graphene and topological
insulators, and its band structure—two conical bands touching at a single point—has also …