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 …

We give a general overview of the high-frequency regime in periodically driven systems and
identify three distinct classes of driving protocols in which the infinite-frequency Floquet …

Unitary circuits subject to repeated projective measurements can undergo an entanglement
phase transition (EPT) as a function of the measurement rate. This transition is generally …

Many-body localization (MBL), the disorder-induced localization of interacting particles,
signals a breakdown of conventional thermodynamics because MBL systems do not …

We identify an unconventional algebraic scaling phase in the quantum dynamics of long-
range hopping, free fermions, which are exposed to continuous local measurements. The …

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 …

We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices
using laser-assisted tunneling and a potential energy gradient provided by gravity or …

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 …

Ultracold quantum gases offer a unique setting for quantum simulation of interacting many-
body systems. The high degree of controllability, the novel detection possibilities and the …

We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-
dimensional quasiperiodic potential, which in the noninteracting limit exhibits an …