Impact of Double Noise on Kinetic Parameters in the Kick Rotor Model

We then proceed to investigate the impact of double noise on various kinetic parameters in the kick rotor model, including the inverse participation rate, fidelity, and OTOC operator. Through numerical analysis of the evolution of these dynamic variables under different Levy parameters, we discovered that noise with positive autocorrelation can impede the changes in these variables. This effect is more pronounced when the Levy parameter is larger, which is consistent with the momentum variance results. This trend is also observed in the inverse participation rate and fidelity parameters, where the initial decay is exponential and the asymptotic decay is a power law. Additionally, the decay of the system under red noise is the slowest, while the decays under blue and purple noise show no significant changes. The OTOC operator reflects the system's degree of chaos, where red and pink noise with positive autocorrelation slow down diffusion, while blue and purple noise with negative autocorrelation have the opposite effect. These findings demonstrate that the autocorrelation of colored noise can affect the quantum chaotic properties of the system.