发表机构
Mandelstam Institute for Theoretical Physics, School of Physics, University of the Witwatersrand; Instituto de Física Teórica UAM/CSIC（曼德尔斯坦理论物理研究所，物理学系，威特沃特斯兰德大学; UAM/CSIC理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建了关联传播复杂度与局域谱统计的解析框架，明确了传播复杂度有限时间峰值的谱起源，适用于混沌与可积系统，建立了Krylov动力学与谱统计的联系。
AI 中文摘要
传播复杂度已成为探究量子混沌的有效探针，但其特征有限时间峰值的微观谱起源尚未完全明晰。我们构建了将传播复杂度与局域谱统计直接关联的解析框架。从Krylov核的能量空间表象出发，我们证明该核近似为带状，从而形成由有序谱中邻近能级主导的快速收敛对角展开。受此结构启发，我们提出近似核普适性假设：经展开后，Krylov核可由均匀晶格的核良好近似。将该普适核与局域谱统计结合，我们得到传播复杂度的简单解析表达式，其形式为第k近邻间距分布的傅里叶变换。特别地，在主导阶下，有限时间峰值由最近邻间距分布的傅里叶变换控制。该框架既适用于混沌随机矩阵系综，也适用于可积泊松极限，明确了复杂度峰值及其后期行为的谱起源，并建立了Krylov动力学与谱统计的直接关联。
英文摘要
Spread complexity has emerged as a useful probe of quantum chaos, yet the microscopic spectral origin of its characteristic finite-time peak remains incompletely understood. We develop an analytic framework that relates spread complexity directly to local spectral statistics. Starting from an energy-space representation of the Krylov kernel, we show that the kernel is approximately banded, leading to a rapidly convergent diagonal expansion dominated by nearby levels in the ordered spectrum. Motivated by this structure, we propose an approximate kernel-universality hypothesis: after unfolding, the Krylov kernel is well approximated by that of a uniform lattice. Combining this universal kernel with local spectral statistics yields a simple analytic expression for spread complexity in terms of the Fourier transforms of the $k$-th nearest-neighbour spacing distributions. In particular, at leading order, the finite-time peak is controlled by the Fourier transform of the nearest-neighbour spacing distribution. The resulting framework describes both chaotic random-matrix ensembles and the integrable Poisson limit, identifies the spectral origin of the complexity peak and its late-time behaviour, and provides a direct connection between Krylov dynamics and spectral statistics.
Comments19 pages, 13 figures. A new section has been added, and the manuscript has been reformatted in a double-column layout
