Impact of Dual Noise on Dynamical Localization in the Kick Rotor Model

The kick rotor model is a common dynamical foundation model used to study classical and quantum chaos behavior. This model exhibits rich dynamical properties, where in the classical case, chaos phenomena occur, while in the quantum case, dynamical localization occurs. The study of dynamical localization in the kick rotor model contributes to a better understanding of quantum chaos and decoherence properties. To further investigate the influence of noise on the system's dynamical properties, this paper introduces colored noise as amplitude noise based on the study of the impact of Levy noise on the dynamical localization of the kick rotor model. The study investigates the effect of the dual noise of temporal noise (Levy noise) and amplitude noise (colored noise) on the dynamical localization of the kick rotor model, providing a potential path to further suppress the growth of decoherence rates.