{
  "abstract": "This work provides a complete analytical characterization of the transfer- matrix structure associated with the finite Kronig-Penney model consisting of one-dimensional arrays of Dirac delta potentials recently introduced by Figueroa et al. (2025). Although their study identified the emergence of specific transfer-matrix entries and related combinatorial coefficients, a rig- orous derivation of the corresponding closed-form expressions has not yet been established. By expressing the N th power of the unit-cell transfer ma- trix in terms of Chebyshev polynomials of the second kind, we obtain explicit closed-form representations for the global transmission and reflection ampli- tudes. The proposed formulation reveals a previously unrecognized structural correspondence between multiple quantum scattering processes, discrete con- volutional patterns, and hypercomplex combinatorial structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08523",
  "author_total": 3,
  "authors": [
    {
      "name": "Lidia Aceto"
    },
    {
      "name": "Pietro Antonio Grassi"
    },
    {
      "name": "Helmuth Robert Malonek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ana5wde23t7mp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08523",
  "fulltext_url": null,
  "id": "ana5wde23t7mp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08523",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7212075998",
  "pdf_url": "https://arxiv.org/pdf/2609.08523",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ana5wde23t7mp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.08523",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08523"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Arithmetic triangular structures in the transfer-matrix of finite Kronig-Penney models",
  "title_text": "Arithmetic triangular structures in the transfer-matrix of finite Kronig-Penney models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/ana5wde23t7mp",
  "venue": "arXiv",
  "versions": []
}