The synergy between non-Hermitian concepts and topological ideas have led to very fruitful
activity in the recent years. Their interplay has resulted in a wide variety of new non …

We develop a theory of symmetry in open quantum systems. Using the operator-state
mapping, we characterize symmetry of Liouvillian superoperators for the open quantum …

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

The spectral statistics of non-Hermitian random matrices are of importance as a diagnostic
tool for chaotic behavior in open quantum systems. Here, we investigate the statistical …

This is part II of a review relating to the three classes of random non-Hermitian Gaussian
matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre …

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

Studies of many-body non-Hermitian parity-time (PT)-symmetric quantum systems are
attracting a lot of interest due to their relevance in research areas ranging from quantum …

Real eigenvalues of pseudo-Hermitian matrices, such as real matrices and PT− symmetric
matrices, frequently split into complex conjugate pairs. This is accompanied by the breaking …

Identifying phase boundaries of interacting systems is one of the key steps to understanding
quantum many-body models. The development of various numerical and analytical methods …

The classification of point gap topology in all local non-Hermitian (NH) symmetry classes
has been recently established. However, many entries in the resulting periodic table have …