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 Hermiticity condition in quantum mechanics required for the characterization of (a)
physical observables and (b) generators of unitary motions can be relaxed into a wider class …

We discuss recent research on quantum transport in complex materials, from photosynthetic
light-harvesting complexes to photonic circuits. We identify finite, disordered networks as the …

We introduce a wave front sha** protocol for focusing inside disordered media based on a
generalization of the established Wigner-Smith time-delay operator. The key ingredient for …

We suggest a method of studying the joint probability density (JPD) of an eigenvalue and the
associated 'non-orthogonality overlap factor'(also known as the 'eigenvalue condition …

We study the overlaps between eigenvectors of nonnormal matrices. They quantify the
stability of the spectrum, and characterize the joint eigenvalues increments under Dyson …

The Hamilton operator of an open quantum system is non-Hermitian. Its eigenvalues are
generally complex and provide not only the energies but also the lifetimes of the states of the …

We study the mean diagonal overlap of left and right eigenvectors associated with complex
eigenvalues in $ N\times N $ non-Hermitian random Gaussian matrices. In well known …

The eigenvalues of a non-Hermitian Hamilton operator are complex and provide not only the
energies but also the lifetimes of the states of the system. They show a nonanalytical …

The non-Hermitian matrix-valued Brownian motion is the stochastic process of a random
matrix whose entries are given by independent complex Brownian motions. The bi …