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
本研究在随机自由费米子中精确求解本征态热化的两点重叠统计，证明平滑包络不决定细粒度涨落，并给出精确闭式结果。
AI 中文摘要
本征态热化约束了可观测量对能量的平滑依赖，但其本身并不确定多体本征态与选定基之间重叠的微观统计：平滑包络是一点陈述，而它未确定的涨落场携带结构化的两点协方差。我们建立了这一区分，并在随机自由费米子中精确求解了该涨落场——这是一个由高斯正交单粒子哈密顿量构建的斯莱特行列式本征态系综，其本征态热化由Magán建立。在该系综中，每个通道的重叠是Haar分布正交矩阵的子式，因此其统计遵循经典随机矩阵理论。一点定律对每个通道都精确平坦，具有精确的矩层级，且并非Porter-Thomas形式：小强度以代数方式增强，而非通过指数Porter-Thomas形式；平均扇区携带负的、阶数为1的纯归一化起源的关联修正。两点协方差在Gaussian不动点处精确闭合：它由两个本征态共享的单体模式数和两个通道共享的模式数组织，其能量分辨形式因子分解为该几何结构乘以单粒子半圆的经典卷积，两点解析协方差通过积分变换由此得出。精确有限尺寸计算确认了所有闭式形式，字典的结构恒等式在机器精度下成立。这些结果提供了本征态热化的多解析描述所依据的两点涨落扇区的精确可解微观实现：平滑包络并不决定细粒度涨落。
英文摘要
Eigenstate thermalization fixes the smooth energy-resolved envelope of few-body observables but not the microscopic overlap statistics that realize it. In the multi-resolvent hierarchy, this missing information appears in a two-resolvent fluctuation sector. We solve that sector exactly in a tractable benchmark, random free fermions, obtaining a non-Porter-Thomas intensity hierarchy, a structured channel-distance covariance, and an exact overlap kernel that closes the two-resolvent covariance. We then reconstruct the same sector without using its exact solution: a projected self-consistency scheme fixes the irreducible vertex through independently computable projections, while unconstrained residuals identify the sectors missed by a minimal ansatz and are completed exactly by a finite-size Weingarten evaluation, without fitting. For interacting deformations, we prove a model-independent moment identity showing that the deep-plane coefficients are fixed by Hamiltonian-moment covariances. This yields an exact rigidity law: pair-hopping interactions freeze the sector, dense perturbations add only an isotropic layer, and density-density interactions produce an explicit polynomial deformation in channel geometry. By contrast, the bulk sector requires the interacting eigenstate-overlap kernel and exhibits a logarithmically divergent perturbative response. The fluctuation sector therefore splits into a rigid moment-determined part and an intrinsically nonperturbative eigenstate-resolved part.
Comments37 pages, 4 figures
