Quantum Mpemba effect in quasiperiodic systems

We study a one-dimensional quasiperiodic tight-binding model with simultaneous off-diagonal (hopping) and diagonal (onsite) modulations. Using the inverse participation ratio and the wave-packet centroid, we construct localization-delocalization phase diagrams for both equilibrium and nonequilibrium steady states. We analyze the robustness of initial-state properties under dissipation and characterize dissipation-induced localization-delocalization transitions (and their reversals) in detail. Trace-distance dynamics provide evidence for a quantum Mpemba effect: states prepared farther from the steady state can relax faster than states initialized closer to it. We propose a starting-line hypothesis that explains the presence or absence of this effect across parameter regimes. These results advance the understanding of steady-state phase transitions and relaxation dynamics in dissipatively driven quasiperiodic systems.