{
  "abstract": "In this paper, we investigate the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity formulated on a three dimensional Riemannian manifold. We derive the gap equation in the path integral picture by employing a Hubbard-Stratonovich transformation followed by a saddle point approximation. Under the assumption that the length scale set by the metric is much larger than the healing length, we solve the gap equation to find a slowly varying gap function that exhibits the effects of curvature. To rigorously address the ultraviolet divergences inherent in the gap equation, we utilize heat kernel expansion techniques, which provide a systematic and mathematically transparent renormalization scheme. We explicitly evaluate the renormalized gap equation at both zero and finite temperatures, computing the relevant integrals asymptotically in the weak-coupling limit ($Δ\\ll μ$). Furthermore, we establish a universal, regularization-independent relation connecting the finite-temperature gap to the zero-temperature gap and the temperature itself. Based on this fundamental relation, we analytically prove the monotonic decrease of the energy gap with increasing temperature ($\\partial Δ/ \\partial T < 0$), successfully recovering the standard universal BCS behavior near the critical temperature within a curved space framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14689",
  "author_total": 3,
  "authors": [
    {
      "name": "Levent Akant"
    },
    {
      "name": "Emine Ertugrul"
    },
    {
      "name": "O. Teoman Turgut"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2b4vsn4xm24w5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14689",
  "fulltext_url": null,
  "id": "2b4vsn4xm24w5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14689",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3104|Physics of Superconductivity and Magnetism"
    ]
  ],
  "openalex": "W7213294844",
  "pdf_url": "https://arxiv.org/pdf/2609.14689",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2b4vsn4xm24w5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14689",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14689"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "BCS Gap Equation on Riemannian Manifolds: A Heat Kernel Analysis",
  "title_text": "BCS Gap Equation on Riemannian Manifolds: A Heat Kernel Analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/2b4vsn4xm24w5",
  "venue": "arXiv",
  "versions": []
}