准周期驱动量子碰撞振子中的混沌特征

中文摘要 AI 辅助

我们证明了在接近擦边条件下，准周期驱动的碰撞振子中会出现量子混沌动力学。虽然先前关于周期驱动下量子碰撞振子的研究报道了奇异非混沌动力学，但我们表明准周期驱动会产生稳健的混沌特征。相应的经典系统经历了一次由擦边引起的从准周期运动到混沌的急剧转变，这一点已通过分岔分析、李雅普诺夫指数、傅里叶谱和0-1检验得到证实。在量子系统中，香农熵时间序列表现出宽带谱，0-1检验值接近1，并且在有理数和无理数驱动频率比下，有限时间李雅普诺夫指数主要为正。独立的量子诊断进一步强化了这一结果：离时有序关联器（OTOC）表现出早期指数增长，其速率几乎相同，而黄金比例驱动导致OTOC的饱和显著加快。保真度表现出一个近似独立于微扰强度的指数衰减区间。这些结果确立了擦边附近的准周期驱动作为产生量子混沌行为的一种机制，并揭示了尽管初始的量子纠缠扩散（scrambling）起始在很大程度上对频率比的有理性不敏感，但后续全局纠缠扩散的发展却受到驱动无理程度的强烈影响。

英文摘要

We demonstrate the emergence of quantum-chaotic dynamics in a quasiperiodically driven impact oscillator near the grazing condition. While previous studies of the quantum impact oscillator under periodic driving reported strange nonchaotic dynamics, we show that quasiperiodic driving produces robust signatures of chaos. The corresponding classical system undergoes a sharp grazing-induced transition from quasiperiodic motion to chaos, as established by bifurcation analysis, Lyapunov exponents, Fourier spectra, and the 0-1 test. In the quantum system, Shannon-entropy time series exhibit broadband spectra, 0-1 test values close to unity, and predominantly positive finite-time Lyapunov exponents for both rational and irrational driving-frequency ratios. Independent quantum diagnostics reinforce this result: the out-of-time-order correlator (OTOC) displays early-time exponential growth with nearly identical rates, while the golden-ratio drive leads to a substantially faster saturation of the OTOC. Fidelity exhibits an exponential decay regime that is approximately independent of perturbation strength. These results establish quasiperiodic driving near grazing as a mechanism for generating quantum-chaotic behavior and reveal that, although the initial onset of scrambling is largely insensitive to frequency-ratio rationality, the subsequent development of global scrambling is strongly influenced by the degree of irrationality of the drive.

发表机构

• Indian Institute of Science Education and Research Kolkata（印度科学教育研究学院加尔各答分校）

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