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

We examine the impact of dual noise on other kinetic parameters in the kick rotor model, specifically the inverse participation rate, fidelity, and OTOC operator. We conduct numerical simulations to track the evolution of these dynamic variables with varying levy parameters. We observe that autocorrelated noise has the potential to impede changes in these variables, especially when the levy parameter is larger. This trend is consistent with the findings on momentum variance. The behavior of the inverse participation rate and fidelity is similar, exhibiting an initial exponential decay followed by a power-law decay. Interestingly, the red noise produces the slowest decay, while blue and purple noise exhibit no remarkable changes. The OTOC operator is indicative of the level of chaos in the system, and we find that red and pink noise with positive autocorrelation slow down diffusion, whereas blue and purple noise with negative autocorrelation have the opposite effect. Our results demonstrate that the autocorrelation of colored noise plays a critical role in shaping the quantum chaotic properties of the system.