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 …

Diffusion driven by temperature or concentration gradients is a fundamental mechanism of
energy and mass transport that inherently differs from wave propagation in both physical …

Phase transitions connect different states of matter and are often concomitant with the
spontaneous breaking of symmetries. An important category of phase transitions is mobility …

One of the most exciting tools that have entered the material science toolbox in recent years
is machine learning. This collection of statistical methods has already proved to be capable …

In this work, we investigate the Anderson localization problems of the generalized Aubry-
André model (Ganeshan-Pixley-Das Sarma's model) with an unbounded quasiperiodic …

Thouless pumping provides one of the simplest manifestations of topology in quantum
systems and has attracted a lot of recent interest, both theoretically and experimentally …

The study of classical wave physics has been reinvigorated by incorporating the concept of
the geometric phase, which has its roots in optics, and topological notions that were …

Non-Hermiticity significantly enriches the properties of topological models, leading to exotic
features such as the non-Hermitian skin effects and non-Bloch bulk-boundary …

Moiré lattices consist of two superimposed identical periodic structures with a relative
rotation angle. Moiré lattices have several applications in everyday life, including artistic …

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 …