{
  "abstract": "We investigate inverse scattering at a fixed energy for semiclassical Schrödinger operators with smooth potentials. For compactly supported potentials satisfying a natural virial condition, we prove that $ \\liminf_{h\\to0} \\|S_1(λ,h)-S_2(λ,h)\\|<\\sqrt{2} $ implies $V_1=V_2$, provided the fixed energy $λ$ lies above both potentials. We then consider radial short-range repulsive potentials. Under a monotonicity assumption on the radial force, we show that the semiclassical differential cross section at a single fixed energy, up to $o(1)$ as $h\\to0$, determines the potential throughout the classically accessible region. Finally, we obtain an analogous rigidity result for nontrapping compactly supported perturbations of the Euclidean metric under a strict convexity assumption.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02175",
  "author_total": 1,
  "authors": [
    {
      "name": "François Nicoleau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5f80cmy74eb6r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02175",
  "fulltext_url": null,
  "id": "5f80cmy74eb6r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02175",
  "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"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7207711584",
  "pdf_url": "https://arxiv.org/pdf/2609.02175",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5f80cmy74eb6r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.02175",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02175"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Inverse Semiclassical Scattering at Fixed Energy",
  "title_text": "Inverse Semiclassical Scattering at Fixed Energy",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:21Z",
  "url": "https://research.draconitic.com/paper/5f80cmy74eb6r",
  "venue": "arXiv",
  "versions": []
}