The paper discusses recent progress in understanding statistical properties of eigenvalues
of (weakly) non-Hermitian and non-unitary random matrices. The first type of ensembles is of …

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

In their preface, the authors state that 'this is a book for absolute beginners'. Well, that
depends on the definition of a beginner! Here,(s) he should be thoroughly at home in …

Sparse non-Hermitian random matrices arise in the study of disordered physical systems
with asymmetric local interactions, and have applications ranging from neural networks to …

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 …

Beam dynamics in synthetic optical media with PT symmetries imposed by a balanced
arrangement of gain or loss is investigated. We find that the beam power evolution is …

To understand the typical dynamics of an open quantum system in continuous time, we
introduce an ensemble of random Lindblad operators, which generate completely positive …

We consider large non-Hermitian N× N matrices with an additive independent, identically
distributed (iid) noise for each matrix elements. We show that already a small noise of …

The eigenstate thermalization hypothesis (ETH) represents a cornerstone in the theoretical
understanding of the emergence of thermal behavior in closed quantum systems. The ETH …