{
  "abstract": "We establish lower bounds on the number of resonances for three-dimensional semiclassical Dirac operators with mass-type potentials. For a pair $\\Dl_j=\\Dl_0+\\mbfβv_j$, $j=1,2$, satisfying the exterior analyticity, decay and non-degeneracy assumptions of the paper, we associate a relative distribution $μ$ to the corresponding mass functions. We prove that if $E_0>1$ is a boundary point of $\\suppμ$, then every complex neighbourhood of $E_0$, and likewise of $-E_0$, contains in total at least $C\\hbar^{-3}$ resonances of the two operators, counted with multiplicity. The proof transfers an analytic wave-front singularity of $μ$ to the relative classical density of states and combines this with Khochman's local trace formula and a relative semiclassical trace formula. As a consequence, if $v$ is a single bounded mass-type potential, analytic with power decay in an exterior sector, with $\\inf(1+v)>0$ and $\\sup v>0$, then $\\Dl=\\Dl_0+\\mbfβv$ has at least $C\\hbar^{-3}$ resonances in every complex neighbourhood of $E_0=1+\\sup v$ and of $-E_0$, for all sufficiently small $\\hbar$. The exponent agrees with Khochman's upper bound, the two resonance families are related by spectral symmetry, and $E_0$ is necessarily a trapping energy. We also prove the relative semiclassical trace formula needed in the argument for general Hermitian matrix-valued perturbations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02356",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhuo Chen"
    },
    {
      "name": "Michael Melgaard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ageknaby28s9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02356",
  "fulltext_url": null,
  "id": "0ageknaby28s9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02356",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7220454489",
  "pdf_url": "https://arxiv.org/pdf/2610.02356",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ageknaby28s9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.02356",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02356"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Lower bound on Dirac resonances with mass-type potentials in the semi-classical limit",
  "title_text": "Lower bound on Dirac resonances with mass-type potentials in the semi-classical limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/0ageknaby28s9",
  "venue": "arXiv",
  "versions": []
}