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 …

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 …

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 …

The bulk-boundary correspondence is among the central issues of non-Hermitian
topological states. We show that a previously overlooked “non-Hermitian skin effect” …

The relation between chiral edge modes and bulk Chern numbers of quantum Hall
insulators is a paradigmatic example of bulk-boundary correspondence. We show that the …

We study a new class of non-Hermitian topological phases in three dimensions in the
absence of any symmetry, where the topological robust band degeneracies are Hopf-link …

Analyses that connect observations of neutron stars with nuclear-matter properties can rely
on equation-of-state insensitive relations. We show that the slope of the binary Love …

Dimensionality plays a fundamental role in the classification of novel phases and their
responses. In generic lattices of 2D and beyond, however, we found that non-Hermitian …

We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes
with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian …

We study topological properties of one-dimensional non-Hermitian systems without chiral
symmetry and give phase diagrams characterized by topological invariants ν E and ν tot …