Double Noise Effects on Dynamical Localization and Decoherence in the Kick Rotor Model

The kick rotor model is a widely used dynamical model for studying classical and quantum chaos. Research on the model's dynamical localization can help us better understand the formation and properties of quantum chaos and decoherence. This paper extends previous research on the influence of Lévy noise on the model's dynamical localization by introducing colored noise as an amplitude noise. Perturbation theory and random phase approximation theory are used to analyze the effect of double noises on the dynamical localization and decoherence rate.

The paper presents several findings. Firstly, the effects of different autocorrelations of colored noise on the dynamical properties of the kick rotor model are investigated. Positive autocorrelation suppresses decoherence, while negative autocorrelation has no significant effect or increases the decoherence rate. This effect is more pronounced when α=2. Secondly, the influence of double noise on other kinetic parameters, including inverse participation rate, fidelity, and OTOC operator, is studied. The noise with positive autocorrelation inhibits changes in these variables, and the effect is more pronounced with larger Lévy parameters. The inverse participation rate and fidelity exhibit exponential initial decay and power law asymptotic decay. The OTOC operator reflects the system's degree of chaos, with red and pink noise with positive autocorrelation slowing down diffusion, while blue and purple noise with negative autocorrelation have the opposite effect.

Overall, this paper provides a pathway to attenuate the decoherence rate in the quantum kick rotor model and highlights the impact of autocorrelation on the system's dynamical properties. The findings have important implications for understanding quantum chaos and decoherence.