{
  "abstract": "For periodic Schrödinger operators $H_V=-Δ+V$ with bounded real-valued potentials on $\\mathbb R^d$ with $d\\ge2$, we show that for generic potentials, each endpoint of every spectral gap is attained by a single Bloch band at only finitely many quasimomenta, and has a nondegenerate Hessian at every attaining point. This proves the Spectral Edge Conjecture for periodic Schrödinger operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30189",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhongkai Tao"
    },
    {
      "name": "Mengxuan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eby9nt087rcbv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30189",
  "fulltext_url": null,
  "id": "eby9nt087rcbv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30189",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
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      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7204870639",
  "pdf_url": "https://arxiv.org/pdf/2608.30189",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eby9nt087rcbv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30189",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30189"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Band edges of periodic Schrödinger operators are generically isolated and nondegenerate",
  "title_text": "Band edges of periodic Schrödinger operators are generically isolated and nondegenerate",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/eby9nt087rcbv",
  "venue": "arXiv",
  "versions": []
}