Paraphrase the following text using more academic and scientific language Use a neutral tone and avoid repetitions of words and phrases：In this work we study the effect of introducing levy noise and c

This research investigates the impact of concurrent introduction of levy noise and colored noise on the quantum kick rotor model's decoherence. It presents a theoretical analysis of the momentum diffusion of the noise-introduced model. The study reveals that introducing positively correlated colored noise can further suppress the decoherence and result in slower momentum diffusion, building on the effectiveness of levy noise in suppressing the decoherence. However, the incorporation of negatively correlated colored noise accelerates the decoherence. Furthermore, the autocorrelation functions of colored noise can influence the chaotic characteristics of quantum systems, similarly affecting momentum diffusion.