Equivalence and superposition of real and imaginary quasiperiodicities

We take non-Hermitian Aubry-Andr\'{e}-Harper models and quasiperiodic Kitaev chains as examples to demonstrate the equivalence superposition of real imaginary potentials (QPs) on inducing localization single-particle states. prove this by analytically computing Lyapunov exponents (or inverse lengths) for systems with purely QPs. Moreover, when superposed same frequency, QPs are coherent localization, under a way which is determined relative phase between them. The induced can be simulated Hermitian model an effective strength QP, implying that in universality class. When their frequencies different relatively incommensurate, they incoherent leads less correlation effects. Numerical results show happens earlier there intermediate mixed lacking mobility edge.