{
  "abstract": "The ground level of the linear $E\\otimes e$ dynamic Jahn-Teller model has long been believed to be the doublet with vibronic angular momentum $j = \\pm\\tfrac12$. We prove that, for arbitrary coupling strength, the $n$th level $E_{nj}$ in the subspace of fixed $j$ strictly increases with $|j|$ for every $n$, $E_{n,1/2} < E_{n,3/2} < E_{n,5/2} < \\cdots$; in particular, the ground level is always the $j = \\pm\\tfrac12$ doublet. The proof uses only a unitary transformation that lowers $j$ by one, combined with the variational principle. We also show that the levels with fixed $j$ are nondegenerate and give explicit lower and upper bounds on the gap $E_{0,j+1} - E_{0j}$. The same Hamiltonian describes Rashba-coupled particles in harmonic traps and, in nuclear physics, the static nucleon in a charged scalar meson field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38190",
  "author_total": 1,
  "authors": [
    {
      "name": "Naoya Iwahara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5q5039b31xgv4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38190",
  "fulltext_url": null,
  "id": "5q5039b31xgv4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38190",
  "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",
      "cond-mat.str-el"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38190",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5q5039b31xgv4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38190",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38190"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Level ordering in the linear $E \\otimes e$ dynamic Jahn-Teller model",
  "title_text": "Level ordering in the linear E ⊗ e dynamic Jahn-Teller model",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/5q5039b31xgv4",
  "venue": "arXiv",
  "versions": []
}