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 …

BACKGROUND Singularities are critical points for which the behavior of a mathematical
model governing a physical system is of a fundamentally different nature compared to the …

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 …

Recent progress on nonlinear properties of parity-time (PT)-symmetric systems is
comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum …

In 1998, Bender and Boettcher found that a wide class of Hamiltonians, even though non-
Hermitian, can still exhibit entirely real spectra provided that they obey parity-time …

The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A
standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity …

Exceptional points are spectral singularities in open quantum and wave systems that exhibit
a strong spectral response to perturbations. This feature can be exploited for a new …

A short résumé is given about the nature of exceptional points (EPs) followed by discussions
about their ubiquitous occurrence in a great variety of physical problems. EPs feature in …

The possibility of parity-time (PT) symmetric periodic potentials is investigated within the
context of optics. Beam dynamics in this new type of optical structures is examined in detail …

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 …