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 …

After many years of development of the basic tools, quantum simulation with ultracold atoms
has now reached the level of maturity at which it can be used to investigate complex …

What happens in an isolated quantum system when both disorder and interactions are
present? Over the recent years, the picture of a non-thermalizing phase of matter, the many …

An interacting quantum system that is subject to disorder may cease to thermalize owing to
localization of its constituents, thereby marking the breakdown of thermodynamics. The key …

Statistical mechanics provides a framework for describing the physics of large, complex
many-body systems using only a few macroscopic parameters to determine the state of the …

Thermalizing quantum systems are conventionally described by statistical mechanics at
equilibrium. However, not all systems fall into this category, with many-body localization …

Over the past decade, there has been remarkable progress in our understanding of
equilibration, thermalization and prethermalization, due in large part to experimental …

Many-body localization is shown to suppress the imaginary parts of complex eigenenergies
for general non-Hermitian Hamiltonians having time-reversal symmetry. We demonstrate …

We show that weak measurements can induce a quantum phase transition of interacting
many-body systems from an ergodic thermal phase with a large entropy to a nonergodic …

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting
quantum spin models. Effective spins are represented by appropriate internal energy levels …