We investigate localization transition in an open quasiperiodic ladder where the quasiperiodicity is described by the Aubry-André-Harper model. While previous studies have shown that higher-order hopping or constrained quasiperiodic potentials can induce a mixed-phase zone in one dimension, we demonstrate that the dissipation can induce mixed phase zone in a one dimensional nearest-neighbor system without imposing any explicit constraints on the quasiperiodic potential or hopping param- eter. Our approach exploits an exact correspondence between the eigenspectrum of the Liouvillian superoperator and that of the non-Hermitian Hamiltonian, valid for quadratic fermionic systems under linear dissipation. Using third quantization approach within Majorana fermionic represen- tation, we analyze three dissipation configurations: alternating gain and loss applied to every site, to alternate sites, and to each site of a single strand under balanced and imbalanced conditions. By computing the inverse and normalized participation ratios, we show that dissipation can drive the system into three distinct phases: delocalizd, mixed, and localized. Notably, the mixed-phase zone is absent for balanced dissipation applied at every site or along a single strand but emerges upon introducing imbalance, while for alternate site dissipation it appears in both balanced and imbalanced cases. Furthermore, the critical points and the width of the mixed-phase window can be selectively tuned by varying the dissipation strength. These findings reveal that the dissipa- tion plays a decisive role in reshaping localization transitions in quasiperiodic systems, offering new insight into the interplay between non-Hermitian effects and quasiperiodic order.
Sarkar et al. (Thu,) studied this question.