Impact of Colored Noise on Dynamical Localization and Chaotic Properties of the Kick Rotor Model

Noise typically causes the kick rotor model to experience exponential decay of coherence, whereas the Levy kick rotor model exhibits power-law decay of coherence. To investigate the influence of noise on the dynamic properties of the system, this study introduces colored noise as amplitude noise and examines the impact of dual noise, including Levy noise and colored noise, on the dynamical localization and chaotic properties of the kick rotor model. The variations of momentum variance mean and OTOC operator under different colored noise influences are calculated. Numerical calculations demonstrate that the positive autocorrelation of colored noise can further suppress momentum diffusion, providing a potential pathway to curb the growth of decoherence rate.