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 …

In spatially periodic Hermitian systems, such as electronic systems in crystals, the band
structure is described by the band theory in terms of the Bloch wave functions, which …

In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary Bloch band theory
and Bloch topological invariants fail to correctly predict energy spectra, topological boundary …

A unique feature of non-Hermitian (NH) systems is the NH skin effect, ie, the edge
localization of an extensive number of bulk-band eigenstates in a lattice with open or semi …

In this Letter, we study the conditions under which on-site dissipations can induce non-
Hermitian skin modes in non-Hermitian systems. When the original Hermitian Hamiltonian …

Higher-order topology realizes topologically robust corner modes as a manifestation of
nontriviality. We theoretically propose non-Hermitian skin effects which stem from the …

Both theoretical and experimental studies of topological phases in non-Hermitian systems
have made a remarkable progress in the last few years of research. In this article, we review …

Knots have a twisted history in quantum physics. They were abandoned as failed models of
atoms. Only much later was the connection between knot invariants and Wilson loops in …

We address the breakdown of the bulk-boundary correspondence observed in non-
Hermitian systems, where open and periodic systems can have distinct phase diagrams …