Impact of Double Noise on Quantum Chaos in the Kick Rotor Model

We investigated the impact of double noise on various kinetic parameters, including inverse participation rate, fidelity, and OTOC operator, in the kick rotor model. By numerically evaluating the evolution of these dynamical variables with different levy parameters, we observed that positive autocorrelated noise can impede the changes of these parameters, and this effect is more pronounced with larger levy parameters, consistent with the momentum variance results. The inverse participation rate and fidelity exhibited similar behavior, with initial exponential decay and asymptotic power law decay. Additionally, the system decayed slower with red noise, while blue and purple noise showed no significant difference. The OTOC operator serves as a measure of the system's chaos, with red and pink noise with positive autocorrelation slowing down diffusion, while blue and purple noise with negative autocorrelation had the opposite effect. These results demonstrate that the autocorrelation of colored noise plays a crucial role in shaping the quantum chaotic properties of the system.