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arXiv:2212.09194

Scaling of out-of-time ordered correlators in a non-Hermitian kicked rotor model

Wen-Lei Zhao, Ru-Ru Wang

Published Dec 18, 2022• 0 citations
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Abstract

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 $\mathcal{PT}$-symmetry. The spontaneous $\cal{PT}$-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 $\cal{PT}$ 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.

DOI
10.48550/arxiv.2212.09194

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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 PT\mathcal{PT}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 GGG features a quantized response to the increase of the kick strength KKK. 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.
We investigate both theoretically and numerically the dynamics of out-of-time-ordered correlators (OTOCs) in quantum resonance conditions for a kicked rotor model. We employ various operators to construct OTOCs in order to thoroughly quantify their commutation relation at different times, therefore unveiling the process of quantum scrambling. With the help of quantum resonance condition, we have deduced the exact expressions of quantum states during both forward evolution and time reversal, which enables us to establish the laws governing OTOCs' time dependence. We find interestingly that the OTOCs of different types increase in a quadratic function of time, breaking the freezing of quantum scrambling induced by the dynamical localization under non-resonance condition. The underlying mechanism is discovered, and the possible applications in quantum entanglement are discussed.
We numerically investigate the quantum transport in coupled kicked rotors with PT\mathcal{PT}PT-symmetric potential. We find that spontaneous PT\mathcal{PT}PT-symmetry breaking of wave functions emerges when the amplitude of the imaginary part of the complex potential is beyond a threshold value, which can be modulated by the coupling strength effectively. In the regime of PT\mathcal{PT}PT-symmetry breaking, the particles driven by the periodical kicks move unidirectionally in momentum space, indicating the emergence of a directed current. Meanwhile, with increasing the coupling strength, we find a transition from the ballistic energy diffusion to a kind of modified ballistic energy diffusion where the width of the wave packet also increases with time in a power law. Our findings suggest that the decoherence effect induced by the interplay between the interparticle coupling and the non-Hermitian driving potential is responsible for these particular transport behaviors.
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