Wigner distribution, Wigner entropy and Quantum Refrigerator of a One-Dimensional Off-diagonal Quasicrystal

We investigate an off-diagonal quasicrystal featuring simultaneous off-diagonal and diagonal quasiperiodic modulations. By analyzing the fractal dimension, we map out the delocalization-localization phase diagram. We demonstrate that delocalized and localized states can be distinguished via the Wigner distribution, while extended, critical, and localized phases are separated using the Wigner entropy. Furthermore, we explore the quantum thermodynamic properties, revealing that localized states facilitate the emergence of a quantum heater mode, alongside the appearance of a refrigerator mode. These findings enhance our understanding of localization phenomena and expand the thermodynamic applications of quasiperiodic systems.