{
  "abstract": "We consider the two-dimensional Dirac operator with constant magnetic field that is perturbed by a combination of electrostatic and Lorentz-scalar delta interactions with variable coefficients supported on a smooth closed curve. Self-adjointness is studied in the so-called non-critical and critical cases. In the non-critical case the essential spectrum is unchanged-it remains to be the set of the Landau-Dirac levels, the eigenvalues of infinite multiplicity of the unperturbed operator-while in the critical case an additional interval of essential spectrum emerges in the spectral gap containing zero. Our main result concerns the discrete spectrum in the non-critical case: using the pseudodifferential properties of the involved boundary integral operators, we show that the eigenvalues accumulate at each Landau-Dirac level at a rate governed by the logarithmic capacity of the curve. A novel and surprising phenomenon is the change in the side of the accumulation depending on the position relative to the critical value. As a byproduct, clusters of eigenvalues for a family of exterior boundary value problems are obtained via confining couplings; the infinite-mass boundary condition arises as a special case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.20665",
  "author_total": 3,
  "authors": [
    {
      "name": "Badreddine Benhellal"
    },
    {
      "name": "Vincent Bruneau"
    },
    {
      "name": "Pablo Miranda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fgb7eq3vt16k0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.20665",
  "fulltext_url": null,
  "id": "fgb7eq3vt16k0",
  "issns": [
    "1664-039X",
    "1664-0403"
  ],
  "landing_url": "https://hal.science/hal-05785849v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7204090181",
  "pdf_url": "https://hal.science/hal-05785849/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-21",
  "publisher": "European Mathematical Society",
  "ris": "https://research.draconitic.com/paper/fgb7eq3vt16k0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:50Z",
      "native_id": "hal-05785849",
      "source": "hal",
      "url": "https://hal.science/hal-05785849v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Spectral Theory in Mathematical Physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The Landau-Dirac operator with shell interactions: self-adjointness and clustering",
  "title_text": "The Landau-Dirac operator with shell interactions: self-adjointness and clustering",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:50Z",
  "url": "https://research.draconitic.com/paper/fgb7eq3vt16k0",
  "venue": "Journal of Spectral Theory",
  "versions": []
}