Sensitivity and Pseudospctra of Non-Hermiitan Quasi-Periodic Lattices

Localization arises from the inherent randomness within a medium, making it difficult, if not impossible, to analytically study disordered systems. To address this, models like the Aubry-André-Harper (AAH) model [1]–[3] have been developed. This model is a perfect platform for exploring one-dimensional quasicrystals and showcases a striking metal-insulator phase transition at a critical quasiperiodic potential strength [2], [3]. We extend this model to the non-Hermitian quasiperiodic AAH system with onsite gain and loss (NHAAH), revealing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathscr{P} \mathscr{T}$</tex>-symmetry phase transitions and the formation of exceptional points (EPs), which exhibit high sensitivity to external perturbations. The generalized eigenspectrum is particularly suited for non-Hermitian systems, where the pseudospectrum deviates significantly from the eigenspectrum [4]. We examine the spectral sensitivity of even and odd lattices through the lens of pseudospectra analysis, uncovering deeper insights into the system's dynamics and stability [5].