Mathematical analysis

Winding number

Chemistry

Quasicrystal

Biochemistry

Physics

Pure mathematics

Mathematics

Hermitian matrix

Gene

Quantum mechanics

Transition (genetics)

Condensed matter physics

Spectrum (functional analysis)

Physical review. B./Physical review. B

By analyzing the Lyapunov exponent, the authors develop here a general scheme for the study of one-dimensional non-Hermitian quasicrystals. Based on Avila's global theory, they establish a correspondence between a series of non-Hermitian quasicrystals and their corresponding Hermitian models, which allows them to obtain the phase transition properties of non-Hermitian systems just by studying the corresponding Hermitian cases. They also unveil an intriguing feature in the robust spectrum and the intrinsic relation between the winding number and slope of the Lyapunov exponent.

Localization transition, spectrum structure, and winding numbers for one-dimensional non-Hermitian quasicrystals