纠缠支配投影系综中随机性的早期增长
Entanglement governs early-time growth of randomness in projected ensembles
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中文总结 AI 辅助
该研究揭示纠缠是投影系综中随机性早期增长的支配机制，通过框架势量化短时间动力学，建立局部与全局随机性的直接联系，阐明局部随机性源于全局量子动力学。
中文摘要 AI 辅助
深度热化关注投影系综在晚期出现的通用纯态统计，但支配随机性初始增长的机制仍不清楚。本文研究由初始非纠缠态生成的投影系综的短时间动力学，用框架势量化其随机性。对于任意哈密顿量，只要初始浴态在测量基下具有完全支撑，我们证明时间三次方阶的框架势完全由子系统纯度决定，进而由未测量子系统与其补集之间产生的双partite纠缠决定。因此，纠缠时间尺度设定了局部随机性增长的初始时间尺度，且与浴测量基无关。对于幺正不变的哈密顿量系综，我们进一步将k阶投影系综框架势与4k点谱形状因子关联，或等价地与全局幺正动力学的2k阶框架势关联，建立了局部与全局随机性的直接联系。我们的结果确定纠缠是支配投影系综中随机性 onset 的机制，并阐明局部随机性如何从全局量子动力学中产生。
英文摘要
Deep thermalization concerns the emergence of universal pure-state statistics in projected ensembles at late times, yet the mechanism governing the initial growth of randomness remains unclear. Here, we study the short-time dynamics of projected ensembles generated from initially unentangled states, quantifying their randomness using frame potentials. For arbitrary Hamiltonians, provided the initial bath state has full support in the measurement basis, we show that the frame potentials to cubic order in time are determined entirely by the subsystem purity, and hence by the bipartite entanglement generated between the unmeasured subsystem and its complement. The entanglement timescale therefore sets the initial timescale for the growth of local randomness, independently of the bath measurement basis. For unitarily invariant Hamiltonian ensembles, we further relate the projected-ensemble frame potential at order $k$ to the $4k$-point spectral form factor, or equivalently to the $2k$th frame potential of the global unitary dynamics, establishing a direct connection between local and global randomness. Our results identify entanglement as the mechanism governing the onset of randomness in projected ensembles and clarify how local randomness emerges from global quantum dynamics.
