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 …

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-
reaching physical consequences observable in a range of dissipative settings are reviewed …

Bulk–boundary correspondence, a guiding principle in topological matter, relates robust
edge states to bulk topological invariants. Its validity, however, has so far been established …

A random walk is known as a random process which describes a path including a
succession of random steps in the mathematical space. It has increasingly been popular in …

Quantum random walk is the quantum counterpart of a classical random walk. The classical
random walk concept has long been used as a computational framework for designing …

In the standard quantum theory, the causal order of occurrence between events is
prescribed, and must be definite. This has been maintained in all conventional scenarios of …

We predict novel topological phases with broken time-reversal symmetry supporting the
coexistence of opposite chiral edge states, which are fundamentally different from the …

The notion of non-Hermitian optics and photonics rooted in quantum mechanics and
photonic systems has recently attracted considerable attention ushering in tremendous …

The out-of-time-ordered correlators (OTOC), a fundamental concept for quantifying quantum
information scrambling, has recently been suggested to be an order parameter to …

Quantum topological photonics is a new research field with great potential that is based on
developments in both quantum optics and topological photonics. Topological photonics …