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 …

Quantum information processing relies on the precise control of non-classical states in the
presence of many uncontrolled environmental degrees of freedom. The interactions …

The density-matrix renormalization group method (DMRG) has established itself over the
last decade as the leading method for the simulation of the statics and dynamics of one …

The study of open quantum systems–microscopic systems exhibiting quantum coherence
that are coupled to their environment–has become increasingly important in the past years …

Recent experimental developments in diverse areas—ranging from cold atomic gases to
light-driven semiconductors to microcavity arrays—move systems into the focus which are …

The realization of Bose Einstein condensates (BEC) and quantum degenerate Fermi gases
with cold atoms has been a highlight of quantum physics during the past decade. Cold …

Fermionic alkaline-earth atoms have unique properties that make them attractive candidates
for the realization of atomic clocks and degenerate quantum gases. At the same time, they …

Originally, the Hubbard model was derived for describing the behavior of strongly correlated
electrons in solids. However, for over a decade now, variations of it have also routinely been …

Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian
(NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering …

When a quantum system initialized in a product state is subjected to either coherent or
incoherent dynamics, the entropy of any of its connected partitions generically increases as …