标题： 时间有序关联函数对于威格纳矩阵 显示英文标题

标题： Out-of-time-ordered correlators for Wigner matrices

摘要： 我们考虑在由随机Wigner矩阵作为哈密顿量描述的平均场混沌量子系统中，两个一般可观测量$A$和$B$的时间演化反序关联函数（OTOC）。我们严格识别了由物理上有意义的编织时间和弛豫时间分隔的三个时间区域。我们分析的主要特点是，我们将误差项表示为可观测量的最优Schatten（迹）范数，使我们能够跟踪误差对其秩的精确依赖关系。特别是，对于显著重叠且低秩的可观测量，OTOC被证明在编织时间表现出显著的局部最大值，这一特征可能在物理学文献中之前未被注意到。我们的主要工具是一种新颖的多解析器局部定律，结合Schatten范数，统一并改进了以前涉及更粗糙的算子范数（参见[G. Cipolloni, L. Erdős, D. Schröder. Elect. J. Prob. 27, 1-38, 2022]）或Hilbert-Schmidt范数（参见[G. Cipolloni, L. Erdős, D. Schröder. Forum Math., Sigma 10, E96, 2022]）的局部定律。 显示英文摘要

摘要： We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables $A$ and $B$ in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [G. Cipolloni, L. Erd\H{o}s, D. Schr\"oder. Elect. J. Prob. 27, 1-38, 2022]) or the Hilbert-Schmidt norm (cf. [G. Cipolloni, L. Erd\H{o}s, D. Schr\"oder. Forum Math., Sigma 10, E96, 2022]).