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 topological properties of an object, associated with an integer called the topological
invariant, are global features that cannot change continuously but only through abrupt …

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 the past decade, the concept of parity-time $(\mathcal {PT}) $ symmetry, originally
introduced in non-Hermitian extensions of quantum mechanical theories, has come into …

Exceptional points (EPs) are singularities that arise in non-Hermitian physics. Current
research efforts focus only on systems supporting isolated EPs characterized by increased …

Dissipation in mechanics, optics, acoustics, and electronic circuits is nowadays recognized
to be not always detrimental but can be exploited to achieve non-Hermitian topological …

Controlling light transport in nonlinear active environments is a topic of considerable interest
in the field of optics. In such complex arrangements, of particular importance is to devise …

By utilizing the vector nature of light as well as the inherent anisotropy of artificial meta-
atoms, we investigate parity time symmetry breaking in polarization space using a …

When a planar dielectric medium has a permittivity profile that is an analytic function in the
upper or lower half of the complex position plane x= x′+ ix ″then the real and imaginary …