Paraphrase the following text using more academic and scientific language Use a neutral tone and avoid repetitions of words and phrases：In the absence of noise OTOC demonstrates exponential diffusion

In the absence of external disturbances, the Out-of-Time-Ordered Correlator (OTOC) exhibits an exponential diffusion pattern during the initial stages of evolution, eventually reaching a magnitude of $10^4$ within a period of 30. This pattern is consistent with the classical case. Subsequent to this initial phase, the OTOC diffusion curve undergoes a clear transition from exponential to power-law growth, characterized by a smaller power-law growth coefficient and periodic fluctuations during the later stages of evolution. The introduction of colored noise into the quantum kick rotor model leads to a significant acceleration in the growth rate of OTOC, resulting in faster power-law diffusion with a Levy parameter of $\alpha=0.5$, and exponential growth with $\alpha=2.0$. The effect of this colored noise on the growth behavior of OTOC is akin to its influence on momentum diffusion, implying that the chaotic nature of the kick rotor model is also impacted by autocorrelation.