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 …

Recent decades have witnessed great developments in the field of quantum simulation—
where synthetic systems are built and studied to gain insight into complicated, many-body …

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the
experimental investigation of ultracold gases made of highly magnetic atoms has …

Simulating quantum mechanics is known to be a difficult computational problem, especially
when dealing with large systems. However, this difficulty may be overcome by using some …

Quantum technologies exploit entanglement to revolutionize computing, measurements, and
communications. This has stimulated the research in different areas of physics to engineer …

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

It is for the first time that quantum simulation for high-energy physics (HEP) is studied in the
US decadal particle-physics community planning, and in fact until recently, this was not …

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 …

Statistical mechanics relies on the maximization of entropy in a system at thermal
equilibrium. However, an isolated quantum many-body system initialized in a pure state …

There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …