Scaling laws of out-of-time-order correlators in a non-Hermitian kicked rotor model - Zhao, Wen-Lei; Wang, Ru-Ru (Frontiers in Physics, 2023)
We investigate the dynamics of the out-of-time-ordered correlators (OTOCs) via a non-Hermitian extension of the quantum kicked rotor model, where the kicking potential satisﬁes PT-symmetry. The spontaneous PT-symmetry breaking emerges when the strength of the imaginary part of the kicking potential exceeds a threshold value. We ﬁnd, both analytically and numerically, that in the broken phase of PT symmetry, the OTOCs rapidly saturate with time evolution. Interestingly, the late-time saturation value scales as a pow-law in the system size. The mechanism of such scaling law results from the interplay between the eﬀects of nonlocal operator in OTOCs and the time reversal induced by non-Hermitian driven potential.