Abstract
This paper reports the findings of the late time behavior of the out-of-time-ordered correlators (OTOCs) via quantum kicked rotor and kicked top models with $\mathcal{PT}$-symmetric driving potential. An analytical expression of the OTOCs' power-law growth with time is yielded as $C(t)=G(K){t}^{\ensuremath{\gamma}}$, with $\ensuremath{\gamma}$ being system dependent. Interestingly, the growth rate $G$ features a quantized response to the increase of the kick strength $K$. The physics behind this is the quantized absorption of energy from the non-Hermitian driving potential. This discovery and the ensuing establishment of the quantization mechanism in the dynamics of quantum chaos with non-Hermiticity will provide insights in chaotic dynamics, promising unprecedented observations in updated experiments.
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