量子混沌多体动力学Kraus映射中的涌现普适性
Emergent universality in Kraus maps of quantum chaotic many-body dynamics
- National University of Singapore（新加坡国立大学）
- California Institute of Technology（加州理工学院）
- Technology Innovation Institute（技术创新研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究在量子混沌多体动力学中发现Kraus映射的涌现普适性，提出单参数随机矩阵假设，并验证其在一维电路中的普适行为，为深度热化提供微观机制。
AI中文摘要：
近期关于“深度热化”的研究揭示了量子多体动力学中超越向吉布斯态平衡的普适物理：通过对其补集进行测量，可以在局部子系统上涌现出最大随机的量子态系综。在本工作中，我们进一步识别了由全局幺正时间演化引起的局部子系统量子动力学“更精细指纹”中所展现的一种新形式的普适性。具体而言，我们考虑投影Kraus系综，即通过关于其补集的经典构型知识对小子系统上的量子通道进行解纠缠而获得的Kraus算子系综。我们的核心结果是一个单参数随机矩阵假设，该假设捕捉了系综在特定时空标度下涌现的统计行为，适用于无守恒律的一般一维电路动力学：该系综由复Ginibre随机矩阵与独立的对数正态随机实标量的乘积描述。前者编码子系统内的加扰，由Ginibre测度的旋转不变性体现，而后者编码Born概率中的涨落，源于底层动力学的局域性。我们的假设可以在由全局Haar随机幺正和双幺正电路生成的动力学特殊情形下得到确立，而对于一般电路，我们利用时空对偶性和空间转移矩阵长乘积上的乘法遍历定理的论证来激发其合理性。对随机和Floquet电路模型的大量数值模拟验证了这些预测。Kraus算子中的这种普适性也为一般一维量子电路动力学中的深度热化提供了微观机制，并对涉及与浴知识相关的经典边信息的局部量子信息可恢复性具有意义。
英文摘要：
Recent studies of "deep thermalization" have revealed universal physics in quantum many-body dynamics beyond equilibration towards Gibbs states: maximally random quantum state ensembles can emerge on local subsystems, generated by measurements on their complement. In this work, we further identify a new form of universality exhibited in the "finer fingerprints" of quantum dynamics for local subsystems, induced by global unitary time-evolution. Specifically, we consider the projected Kraus ensemble, an ensemble of Kraus operators obtained by unraveling the quantum channel on a small subsystem with respect to knowledge of the classical configurations of its complement. Our central result is a one-parameter random matrix Ansatz that captures the ensemble's emergent statistical behavior along particular spacetime scalings, valid for generic 1D circuit dynamics without conservation laws: the ensemble is described by the product of a complex Ginibre random matrix and an independent log-normal random real scalar. The former encodes scrambling within the subsystem, captured by rotational invariance of the Ginibre measure, whereas the latter encodes fluctuations in the Born probabilities, arising from locality of the underlying dynamics. Our Ansatz can be established in the special cases of dynamics generated by global Haar random unitaries and dual-unitary circuits, while we motivate it for generic circuits using arguments of spacetime duality and the multiplicative ergodic theorem on long products of spatial transfer matrices. Extensive numerical simulations for random and Floquet circuit models verify these predictions. This universality in Kraus operators also provides a microscopic mechanism for deep thermalization in generic 1D quantum circuit dynamics, and has implications for local quantum information recoverability involving classical side information tied to knowledge of the bath.
