Quantum mechanics

Function (biology)

Pure mathematics

Topological quantum number

Biology

Gapless playback

Evolutionary biology

Physics

Mathematics

Chern class

Condensed matter physics

Mathematical analysis

Combinatorics

Complex plane

Topology (electrical circuits)

Hermitian matrix

Physical review. B./Physical review. B

Recently, it was shown that non-Hermitian systems, e.g., materials with loss or gain, can have topological properties. Here, the author develops a gauge-independent Green's function approach to classify the topological phases of generic non-Hermitian systems. The proposed theory introduces in a natural way the band gaps of non-Hermitian systems as the strips of the complex-frequency plane, wherein the Green's function is analytical, and unveils that the spectrum of a non-Hermitian topological material cavity terminated with opaque-type walls must be gapless.

Topological theory of non-Hermitian photonic systems