Influence of Colored Noise on Dynamical Localization and Chaos in the Levy Kick Rotor Model

Noise usually causes the kick rotor model to undergo exponential decoherence, while the Levy kick rotor model achieves power-law decay in coherence. To further investigate the impact of noise on the dynamic properties of the system, this paper introduces colored noise as amplitude noise and studies the influence of dual noise, including Levy noise and colored noise, on the dynamical localization and chaotic properties of the kick rotor model. Changes in the mean momentum variance and OTOC operator subjected to different colored noise are calculated. Numerical results show that positive autocorrelation of colored noise can further suppress momentum diffusion, providing a possible path to further inhibit the growth of decoherence rate.