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

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in
controlling dissipation have brought about unprecedented flexibility in engineering non …

We identify an unconventional algebraic scaling phase in the quantum dynamics of long-
range hop**, free fermions, which are exposed to continuous local measurements. The …

Emergence of exceptional points in two dimensions is one of the remarkable phenomena in
non-Hermitian systems. We here elucidate the impacts of symmetry on the non-Hermitian …

Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian
(NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering …

The light-matter interaction can be utilized to qualitatively alter physical properties of
materials. Recent theoretical and experimental studies have explored this possibility of …

Synthetic non-conservative systems with parity-time (PT) symmetric gain–loss structures can
exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity …

A non-Hermitian extension of a Chern insulator and its bulk-boundary correspondence are
investigated. It is shown that in addition to the robust chiral edge states that reflect the …

We propose a novel type of skin effects in non-Hermitian quantum many-body systems that
we dub a “non-Hermitian Mott skin effect.” This phenomenon is induced by the interplay …