This article reviews recent developments in the non-Hermitian skin effect (NHSE),
particularly on its rich interplay with topology. The review starts off with a pedagogical …

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 …

A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity
to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non …

We establish exact relations between the winding of “energy”(eigenvalue of Hamiltonian) on
the complex plane as momentum traverses the Brillouin zone with periodic boundary …

We provide a systematic and self-consistent method to calculate the generalized Brillouin
zone (GBZ) analytically in one-dimensional non-Hermitian systems, which helps us to …

Critical systems represent physical boundaries between different phases of matter and have
been intensely studied for their universality and rich physics. Yet, with the rise of non …

We propose a realistic cold-atom quantum setting where topological localization induces
nonreciprocal pumping. This is an intriguing non-Hermitian phenomenon that illustrates how …

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 …

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical
dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering …

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 …