Noise-Induced Transition to Chaos: Investigating the Impact of Colored Noise on the Out-of-Time-Ordered Correlation Function

The introduction of noise can cause a transition in the system from a localized state to a chaotic state. In the absence of noise, the OTOC operator exhibits exponential growth in the early stages of evolution, increasing to the order of 10^4 within 30 cycles, consistent with exponential growth in classical cases. Subsequently, the growth curve of the OTOC operator shows a clear transition from exponential to power law growth, with a smaller power law growth coefficient in the absence of noise and periodic fluctuations in the later stages of evolution. In the quantum kick rotor model with colored noise, the growth rate of the OTOC operator is significantly accelerated, exhibiting power law growth 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 the OTOC operator is similar to its impact on the momentum diffusion of the system, indicating that the chaotic properties of the system are similarly affected by this autocorrelation.