Impact of Colored Noise on Dynamical Localization and Decoherence in the Kick Rotor Model

The impact of noise on the coherence of the kick rotor model is typically characterized by exponential decay, while the Levy kick rotor model exhibits power-law decay of coherence. This research explores the effects of dual noise sources – colored noise acting as amplitude noise alongside Levy noise – on the dynamical localization and chaotic characteristics of the kick rotor model. To this end, we analyze variations in the momentum variance and out-of-time-order correlation (OTOC) operator under diverse colored noise conditions. Our numerical findings indicate that positive autocorrelation in colored noise can further diminish momentum diffusion, suggesting a potential strategy for reducing the rate of decoherence.