{
  "abstract": "We prove the fixed-potential conjecture of Fefferman, Shapiro, and Weinstein for inversion-symmetric magnetic double wells. We construct a number $L_0>0$ and one smooth, compactly supported, nonpositive, nonradial single-well potential $v$, independent of both the coupling parameter $λ$ and the well displacement, such that for every fixed $L\\ge L_0$ the associated magnetic double-well Hamiltonian has infinitely many exact degeneracies of its two lowest eigenvalues as $λ\\to\\infty$. The magnetic hopping coefficient also vanishes along an infinite sequence tending to infinity. The potential consists of a radial core and two small, reflection-related perturbations supported on one-sided quadratic cusps. Their log-flat profiles isolate two dominant hopping contributions, which we evaluate by steepest descent after inserting the radial ground-state asymptotics. The resulting asymptotic cosine expression, together with error bounds for the even--odd splitting, yields infinitely many exact eigenvalue crossings and changes of ground-state parity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21078",
  "author_total": 6,
  "authors": [
    {
      "name": "Kevin Buck"
    },
    {
      "name": "Charles L. Fefferman"
    },
    {
      "name": "Javier Gómez-Serrano"
    },
    {
      "name": "Amaury Hayat"
    },
    {
      "name": "Jacob Shapiro"
    },
    {
      "name": "Michael I. Weinstein"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f03nxq4vmccrq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21078",
  "fulltext_url": null,
  "id": "f03nxq4vmccrq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21078",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7213939620",
  "pdf_url": "https://arxiv.org/pdf/2609.21078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f03nxq4vmccrq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2609.21078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Double-wells in a strong magnetic field: absence of tunneling for infinitely many values of the coupling constant",
  "title_text": "Double-wells in a strong magnetic field: absence of tunneling for infinitely many values of the coupling constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/f03nxq4vmccrq",
  "venue": "arXiv",
  "versions": []
}