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

We investigated the impact of double noise on various kinetic parameters of the kick rotor model, including inverse participation rate, fidelity, and OTOC operator. Through numerical calculations of the evolution of these dynamic variables with varying levy parameters, we observed that positive autocorrelated noise could suppress changes in these variables. This effect was more pronounced when the levy parameter was larger, consistent with the results for momentum variance. The behaviors of the inverse participation rate and fidelity were similar, with an initial exponential decay followed by a power law asymptotic decay. Additionally, the system decayed slowest with red noise, while the decays with blue and purple noise remained relatively unchanged. The OTOC operator was indicative of the system's degree of chaos, with red and pink noise with positive autocorrelation leading to slower diffusion, while blue and purple noise with negative autocorrelation had the opposite effect. These findings highlight how the autocorrelation of colored noise can impact the quantum chaotic properties of a system.