The past decades have witnessed an explosion of interest in topological materials, and a lot
of mathematical concepts have been introduced in condensed matter physics. Among them …

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 current understanding of the role of topology in non-Hermitian (NH) systems and its far-
reaching physical consequences observable in a range of dissipative settings are reviewed …

A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity
to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non …

We derive field theory descriptions for measurement-induced phase transitions in free
fermion systems. We focus on a multiflavor Majorana chain, undergoing Hamiltonian …

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

Non-Hermiticity gives rise to unique topological phases that have no counterparts in
Hermitian systems. Such intrinsic non-Hermitian topological phases appear even in one …

In this Letter, we study the conditions under which on-site dissipations can induce non-
Hermitian skin modes in non-Hermitian systems. When the original Hermitian Hamiltonian …

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical
dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering …

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