Quantization of Out-of-Time-Ordered Correlators in non-Hermitian Chaotic Systems

TL;DR

This paper investigates the late-time behavior of out-of-time-ordered correlators in a non-Hermitian quantum chaotic system, revealing a quantized growth rate linked to the system's parameters and energy absorption mechanisms.

Contribution

It introduces a novel quantization mechanism in OTOC dynamics within non-Hermitian chaotic systems, supported by analytical and theoretical analysis.

Findings

OTOCs exhibit quadratic growth with a quantized rate

Growth rate G is quantized with respect to kick strength K

Energy absorption from non-Hermitian potential underpins the quantization

Abstract

This letter reports the findings of the late time behavior of the out-of-time-ordered correlators (OTOCs) via a quantum kicked rotor model with $\cal{PT}$-symmetric driving potential. An analytical expression of the OTOCs' quadratic growth with time is yielded as $C(t)=G(K)t^2$. Interestingly, the growth rate $G$ features a quantized response to the increase of the kick strength $K$, which indicates the chaos-assisted quantization in the OTOCs' dynamics. 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.