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

Noise typically causes the kick rotor model to experience exponential decay of coherence, while the Levy kick rotor model exhibits power-law decay of coherence. To further investigate the impact of noise on the system dynamics, this study introduces colored noise as amplitude noise and studies the effects of dual noise containing Levy noise and colored noise on the dynamical localization and chaotic properties of the kick rotor model. The changes in the mean momentum variance and OTOC operator under different colored noise influences are computed. Numerical results indicate that positively autocorrelated colored noise can further suppress momentum diffusion, providing a possible path for further inhibiting the growth of decoherence rates.