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
研究针对 ETH 中光滑函数缺乏微观基础的问题，开发多预解式层次结构，利用递归投影恒等式和 DCA 组织多通道干涉过程，得到统一微观理论，揭示奇偶结构，为量子多体系统热化研究提供新方法。
AI 中文摘要
本研究聚焦于本征态热化假说（ETH），其虽能对孤立量子多体系统的热化进行统计描述，但控制非对角矩阵元能量依赖性的唯象光滑函数$f_O(\bar{E},\omega)$缺乏系统微观基础。为此开发了用于 ETH 光滑函数相关修正的多预解式层次结构，利用递归投影恒等式和对角闭包近似（DCA），按相互作用浴通道数量组织多通道干涉过程，以可系统改进的展开取代对高阶关联的无控制忽略。通过该方法得到 ETH 光滑函数$f_{ji}^2 = D_{ji} + \sum_{r\ge 2} g_{ji}^{(r)}$，并给出了统一、封闭且可系统改进的微观理论。同时，严格的投影和规则约束了整个层次结构，揭示了奇偶结构，表明在量子多体系统中存在可实验测试的特征。
英文摘要
The eigenstate thermalization hypothesis (ETH) parametrizes off-diagonal matrix elements by a smooth function whose microscopic origin remains largely phenomenological. We develop a multi-resolvent hierarchy that derives this smooth structure from the microscopic Hamiltonian. Starting from exact projection identities, we express the ETH variance as $f_{ji}^2=D_{ji}+g_{ji}$, where $D_{ji}$ is the diagonal-overlap baseline and $g_{ji}=\sum_{r\ge2}g_{ji}^{(r)}$ is a systematically improvable hierarchy of multi-channel interference processes. The leading $r=3$ sector generates an odd-parity component in the energy difference, inaccessible to parity-preserving single-resolvent closures. The same resolvent construction yields an exact covariance representation of eigenstate fluctuations. Under amplitude isotropy, decorrelation, and regularity, it reduces to the Gaussian limit, with $q-3=κ_4/\langle c^2\rangle^2$; normalization further fixes the cross-channel covariance $\bar C_i$, including its energy-resolved form. Exact diagonalization verifies these relations in random-matrix and structured systems, while the latter exhibit controlled breakdown of the isotropic Gaussian closure. The framework thus provides a microscopic hierarchy for both the smooth and fluctuation sectors of subsystem ETH.
Comments36 pages
