Impact of Colored Noise on Out-of-Time-Ordered Correlator (OTOC) Diffusion in Quantum Kick Rotor Model

In the absence of noise, the out-of-time-ordered correlator (OTOC) demonstrates exponential diffusion during the early stages of evolution, reaching a magnitude of $10^4$ within 30 periods, which is consistent with the classical case. Subsequently, the diffusion curve of OTOC undergoes a clear transition from exponential to power-law growth, with a smaller power-law growth coefficient in the absence of noise and periodic fluctuations during the later stages of evolution. When colored noise is introduced into the quantum kick rotor model, the growth rate of OTOC is significantly accelerated, demonstrating faster power-law diffusion with a Levy parameter of α=0.5 and exponential growth with α=2.0. The impact of this colored noise on the growth behavior of OTOC is similar to its impact on momentum diffusion, indicating that the chaotic nature of the kick rotor model is also influenced by autocorrelation.