Wigner distribution, Wigner entropy, and quantum refrigerator of a one-dimensional system with off-diagonal and diagonal quasiperiodic modulations

We investigate a one-dimensional system 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. In addition, the efficiency of the quantum engine and the coefficient of performance of the quantum refrigerator are analyzed and discussed. These findings enhance our understanding of localization phenomena and expand the thermodynamic applications of quasiperiodic systems.