{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.19861",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhiqiang Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xeenw6a9e9y5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.19861",
  "fulltext_url": null,
  "id": "5xeenw6a9e9y5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.19861",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
  ],
  "openalex": "W7170188766",
  "pdf_url": "https://arxiv.org/pdf/2607.19861",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xeenw6a9e9y5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2607.19861",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.19861"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Multi-Resolvent Hierarchy for the ETH Smooth Function",
  "title_text": "A Multi-Resolvent Hierarchy for the ETH Smooth Function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/5xeenw6a9e9y5",
  "venue": "arXiv",
  "versions": []
}