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 …

Topological phases of Hermitian systems are known to exhibit intriguing properties such as
the presence of robust boundary states and the famed bulk-boundary correspondence …

We study theoretically the localization properties of two distinct one-dimensional
quasiperiodic lattice models with a single-particle mobility edge (SPME) separating …

Surpassing the individual characteristics of the non-Hermitian skin effect (NHSE) and the
scale-free (SF) effect observed recently, we systematically exploit the exponential decay …

Complex band structure generalizes conventional band structure by also considering
wavevectors with complex components. In this way, complex band structure describes both …

Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their
origin is rooted in local symmetries of the lattice, with destructive interference leading to the …

Fermi-arc surface states of Weyl semimetals exhibit a unique combination of localization to a
surface and the connection to the bulk Weyl fermions. We predict characteristic quantum …

Hyperbolic lattices underlie a new form of quantum matter with potential applications to
quantum computing and simulation and which, to date, have been engineered artificially. A …

We study the decay and oscillations of Majorana fermion wave functions and ground-state
(GS) fermion parity in one-dimensional topological superconducting lattice systems. Using a …

The topological classification of gapped band structures depends on the particular definition
of topological equivalence. For translation-invariant systems, stable equivalence is defined …