Impact of Colored and Levy Noise on Quantum Kick Rotor Model

Firstly, we investigate the impact of colored noise and Levy noise on the quantum kick rotor model, both theoretically and numerically. To generate the color noise, we employ the spectral transformation method and introduce it to the model alongside Levy noise. We then analyze the decoherence factor and momentum variance using perturbation theory and random phase approximation theory, based on the statistical properties of Levy noise and its effect on the dynamical localization. Furthermore, we present numerical results of the momentum variance under different noise types, intensities, and Levy parameters. Our findings indicate that the autocorrelation of the colored noise has varying effects on the dynamical properties of the kick rotor model. Positive autocorrelation further suppresses decoherence, while negative autocorrelation results in either no significant effect or increased decoherence. Moreover, the influence of autocorrelation on the dynamical properties of the system is consistent across different Levy parameters, and most pronounced when α=2.