{
  "abstract": "We consider the linear operator for metamaterial modeling $$L_{c,d }=(χ_{\\RE^{3}\\backslash\\overline Ω}+c)\\nabla\\!\\cdot (χ_{\\RE^{3}\\backslash\\overline Ω}+d)\\nabla\\,,$$ where the material parameters $c>0$ and $d$ are constant on each connected component of the bounded domain $Ω$, $d$ is negative on at least one component of $Ω$ and transmission boundary conditions hold at the interfaces. It turns out that $L_{c,d }$ has, as in the sign-definite case, an absolutely continuous spectrum equal to $[0,+\\infty)$; however, contrary to the latter, it has a non-empty point spectrum; in particular, we find conditions on the parameters so that zero is a threshold eigenvalue. In the case $Ω$ is connected, we study how such a threshold eigenvalue behaves under $\\varepsilon$-small analytic perturbations of the parameters. We show that, depending on the position of the number $\\frac12\\,\\frac{1+d(\\ve)}{1-d(\\ve)}$ relative to the nearest eigenvalue of the Neumann-Poincaré operator of the interface, the zero eigenvalue splits into two branches (analytic in $\\varepsilon^{1/2}$), consisting either of two branches of resonances, or of one branch of negative eigenvalues and one of resonances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18483",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrea Mantile"
    },
    {
      "name": "Andrea Posilicano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8taskm09x1wc4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18483",
  "fulltext_url": null,
  "id": "8taskm09x1wc4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18483",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221805992",
  "pdf_url": "https://arxiv.org/pdf/2610.18483",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8taskm09x1wc4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.18483",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18483"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Sign-indefinite transmission conditions and near-zero eigenvalues and resonances",
  "title_text": "Sign-indefinite transmission conditions and near-zero eigenvalues and resonances",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/8taskm09x1wc4",
  "venue": "arXiv",
  "versions": []
}