{
  "id": "2108.03964",
  "version": "v1",
  "published": "2021-08-09T11:58:22.000Z",
  "updated": "2021-08-09T11:58:22.000Z",
  "title": "Hearing the shape of a magnetic edge in the semiclassical limit",
  "authors": [
    "Wafaa Assaad",
    "Bernard Helffer",
    "Ayman Kachmar"
  ],
  "comment": "34 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues, for the Dirichlet magnetic Laplacian with a non-uniform magnetic field having a jump discontinuity along a smooth curve. The asymptotics hold in the semiclassical limit which also corresponds to a large magnetic field limit, and is valid under a geometric assumption on the curvature of the discontinuity curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-09T11:58:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semiclassical limit",
      "magnetic edge",
      "large magnetic field limit",
      "dirichlet magnetic laplacian",
      "establish accurate eigenvalue asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}