发表机构
School of Physics, Hubei University（湖北大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为随机自由费米子的多分辨关联建立精确副本扇区层级，通过Weingarten代数分解和占据矩阵组装，在任意有限多重性下组织高阶谱累积量，为ETH高阶涨落提供微观基准。
AI 中文摘要
多体本征态对给定通道的谱权重贡献并不由光滑的单点ETH包络固定，其高阶关联——三个及以上通道分辨谱函数的连通累积量——一直缺乏系统化的组织。我们构建了这样一种组织。在随机自由费米子中，每个通道重叠都是Haar正交单体本征矢量矩阵的Slater子式的平方，r-分辨矩允许精确的副本扇区分解：对正交Weingarten代数的双陪集扇区求和，其中置换扇区是副本收缩类，每个扇区值由通道和本征态的重叠模式决定。扇区系数遵循精确的占据矩阵组装——对槽置换的符号卷积、分解为连通块、以及有限态链转移矩阵，其局部转移规则独立于r和k——因此扇区定理在任意有限多重性下成立，在r=3（k=2,3,4）、r=4和r=5（k=2）时精确实现。该结构承载物理层级：完全重合扇区是产生Selberg矩比值q_r的投影，各层级通过精确边缘化嵌套，扇区是分辨累积量背后的多能量谱累积量，以Feshbach阶梯的不可约自能顶点为连通核。因此，随机自由费米子的多分辨关联逐层级地由一个副本扇区代数组织——这是本征态热化高阶涨落扇区的精确微观基准，其微观扇区几何被明确揭示。
英文摘要
The spectral weight with which a many-body eigenstate contributes to a given channel is not fixed by the smooth one-point ETH envelope, and its higher-order correlations---the connected cumulants of three and more channel-resolved spectral functions---have lacked a systematic organization. We construct one. In random free fermions, where every channel overlap is a squared Slater minor of a Haar-orthogonal one-body eigenvector matrix, the $r$-resolvent moment admits an exact replica-sector decomposition: a sum over the double-coset sectors of the orthogonal Weingarten algebra, in which the permutation sectors are the replica contraction classes and each sector value is determined by the overlap pattern of the channels and of the eigenstates. The sector coefficients follow from an exact occupancy-matrix assembly---a signed convolution over the slot permutations, a decomposition into connected blocks, and a finite-state chain transfer matrix whose local transition rules are independent of $r$ and $k$---so the sector theorem holds at arbitrary finite multiplicity, realized exactly at $r=3$ ($k=2,3,4$), $r=4$ and $r=5$ ($k=2$). The structure carries the physical hierarchy: the fully coincident sector is the projection that yields the Selberg moment ratios $q_r$, the levels are nested by exact marginalization, and the sectors are the multi-energy spectral cumulants behind the resolvent cumulants, with the irreducible self-energy vertices of the Feshbach ladder as the connected kernel. The multi-resolvent correlations of random free fermions are therefore organized, level by level, by one replica-sector algebra---an exact microscopic benchmark for the higher-order fluctuation sector of eigenstate thermalization, with its microscopic sector geometry made explicit.
Comments22 pages, 1 figure
