Super-exponential growth of out-of-time-ordered correlators

Out-of-time-ordered correlators (OTOCs) are an effective tool in characterizing black hole chaos, many-body thermalization, and quantum dynamics instability. Previous research findings have shown that the OTOCs' exponential growth (EG) marks limit for systems. However, we report this paper a periodically-modulated nonlinear Schr\"odinger system, which interestingly find way of growth: super-EG. We show OTOCs, stems from chaotic dynamics, will increase super-exponential way. also classical limit, hyper-chaos revealed by linearly-increasing Lyapunov exponent actually triggers super-EG OTOCs. The results break restraints EG as systems, give us insight into nature chaos various fields physics to system.