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Abstract

In this paper, a quasiperiodic system with off-diagonal and diagonal modulations is studied. By analyzing the inverse participation ratio and the centroid position of the wave packet, the delocalization-localization phase diagrams in the equilibrium state and the non-equilibrium steady state are obtained respectively. The stability of the system's initial state on dissipation and the dissipation-driven delocalization-localization transition (or vice versa) are discussed. The dynamic evolution behavior provides evidence for the existence of the quantum Mpemba effect in this dissipation-modulated system. A starting-line hypothesis is proposed, which can be used to explain the occurrence and absence of the quantum Mpemba effect. In addition, the thermodynamic applications of this system have also been studied. The results prove that the localized phase is beneficial to the realization of quantum heater as well. Our work has promoted the understanding of the steady-state phase transitions and dynamic behaviors of dissipation-modulated quasiperiodic systems, and has expanded the existing thermodynamic research on the application of quasiperiodic systems.