{
  "abstract": "We study the fluctuation spectrum and renormalized one-loop quantum mass of the Christ--Lee kink over the full positive range of its deformation parameter. The fluctuation equation is reduced exactly to general-Heun form, yielding parity-resolved continuum solutions and implicit quantization conditions for the discrete spectrum. At the first nontrivial continuum crossing, the odd Heun solution truncates to a polynomial, giving the exact threshold \\(ε_1=\\sqrt{\\sqrt{3}-1}\\). For small deformation, the kink separates into two widely spaced \\(ϕ^6\\)-like interfaces and the fluctuation operator develops a long central cavity. This geometry explains the logarithmic growth of the bound-state count, the asymptotically geometric hierarchy of continuum-threshold crossings, and the emergence of a soft relative-translation mode. In the opposite limit, the spectrum approaches the \\(ϕ^4\\) Pöschl--Teller problem, while its even threshold resonance becomes a shallow bound state at finite deformation. The one-loop correction is evaluated in a fixed vacuum-normal-ordering prescription using a common-regulator spectral trace and independently through an imaginary-frequency functional determinant. The two calculations agree throughout representative finite deformations and reproduce the exact \\(ϕ^4\\) limit. In the small-deformation regime, the extended central region produces a logarithmically enhanced negative quantum correction. These results provide a unified analytic and numerical description of how the spectral reorganization of the Christ--Lee kink controls its semiclassical quantum mass.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27178",
  "author_total": 4,
  "authors": [
    {
      "name": "Mulyanto"
    },
    {
      "name": "Afif Jalu Pradipta"
    },
    {
      "name": "Ardian Nata Atmaja"
    },
    {
      "name": "Bobby Eka Gunara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a1rw6wqagm4t0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27178",
  "fulltext_url": null,
  "id": "a1rw6wqagm4t0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27178",
  "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.MP"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7214237105",
  "pdf_url": "https://arxiv.org/pdf/2609.27178",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a1rw6wqagm4t0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27178",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27178"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Heun Spectrum, Threshold Hierarchy, and One-Loop Quantum Mass of the Christ--Lee Kink",
  "title_text": "Heun Spectrum, Threshold Hierarchy, and One-Loop Quantum Mass of the Christ--Lee Kink",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/a1rw6wqagm4t0",
  "venue": "arXiv",
  "versions": []
}