{
  "abstract": "In this paper, we establish the absence of absolutely continuous spectrum for scalar one-dimensional Laurent operators with multiplicative disorder and critical long-range hoppings. In particular, the requirement of at least quartic off-diagonal decay rate in the existing theory is bypassed by exploiting the finite-difference bound of the convolution kernel, which is available even when the interaction decays only as $|n|^{-1}\\log^{-β}|n|$ with $β>1$. We then apply the abstract main result to a concrete physical model, the capacitance operator in subwavelength physics. For a chain of three-dimensional resonators with one resonator per period, we verify the required decay and finite-difference estimates and conclude the absence of absolutely continuous spectrum. These results leave open the distinction between pure point and singular continuous spectrum, but constitute a key step in proving Anderson localization in wave systems with critical long-range interactions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09582",
  "author_total": 2,
  "authors": [
    {
      "name": "Habib Ammari"
    },
    {
      "name": "Jiayu Qiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ap6xh8at94ryf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09582",
  "fulltext_url": null,
  "id": "ap6xh8at94ryf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09582",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221064109",
  "pdf_url": "https://arxiv.org/pdf/2610.09582",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ap6xh8at94ryf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.09582",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09582"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Absence of Absolutely Continuous Spectrum for One-Dimensional Capacitance Operators with Critical Long-Range Interactions",
  "title_text": "Absence of Absolutely Continuous Spectrum for One-Dimensional Capacitance Operators with Critical Long-Range Interactions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/ap6xh8at94ryf",
  "venue": "arXiv",
  "versions": []
}