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 …

Typically, complex systems are natural or social systems which consist of a large number of
nonlinearly interacting elements. These systems are open, they interchange information or …

We perform a systematic symmetry classification of many-body Lindblad superoperators
describing general (interacting) open quantum systems coupled to a Markovian …

We introduce a complex-plane generalization of the consecutive level-spacing ratio
distribution used to distinguish regular from chaotic quantum spectra. Our approach features …

Spectral correlations are a powerful tool to study the dynamics of quantum many-body
systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix …

This paper contains an exposition of both recent and rather old results on determinantal
random point fields. We begin with some general theorems including proofs of necessary …

The Ginibre unitary ensemble (GinUE) consists of $ N\times N $ random matrices with
independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre …

Random matrix theory is now a big subject with applications in many disciplines of science,
engineering and finance. This article is a survey specifically oriented towards the needs and …

We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, N fermions
with aq-body interaction of infinite range, coupled to a Markovian environment. Close to the …

In this paper, we study the properties of two-dimensional lattices in the presence of non-
Hermitian disorder. In the context of coupled mode theory, we consider random gain-loss …