{
  "id": "2302.08154",
  "version": "v1",
  "published": "2023-02-16T08:56:49.000Z",
  "updated": "2023-02-16T08:56:49.000Z",
  "title": "Propagation for Schrödinger operators with potentials singular along a hypersurface",
  "authors": [
    "Jeffrey Galkowski",
    "Jared Wunsch"
  ],
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "In this article, we study propagation of defect measures for Schr\\\"odinger operators, $-h^2\\Delta_g+V$, on a Riemannian manifold $(M,g)$ of dimension $n$ with $V$ having conormal singularities along a hypersurface $Y$ in the sense that derivatives along vector fields tangent to $Y$ preserve the regularity of $V$. We show that the standard propagation theorem holds for bicharacteristics travelling transversally to the surface $Y$ whenever the potential is absolutely continuous. Furthermore, even when bicharacteristics are tangent to $Y$ at exactly first order, as long as the potential has an absolutely continuous first derivative, standard propagation continues to hold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-16T08:56:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger operators",
      "potentials singular",
      "hypersurface",
      "standard propagation theorem holds",
      "standard propagation continues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}