{
  "id": "2404.02296",
  "version": "v1",
  "published": "2024-04-02T20:48:08.000Z",
  "updated": "2024-04-02T20:48:08.000Z",
  "title": "Quantum Flux and Quantum Ergodicity for Cross Sections",
  "authors": [
    "Hans Christianson",
    "John Toth"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For sequences of quantum ergodic eigenfunctions, we define the quantum flux norm associated to a codimension $1$ submanifold $\\Sigma$ of a non-degenerate energy surface. We prove restrictions of eigenfunctions to $\\Sigma$, realized using the quantum flux norm, are quantum ergodic. We compare this result to known results from \\cite{CTZ} in the case of Euclidean domains and hyperfurfaces. As a further application, we consider complexified analytic eigenfunctions and prove a second microlocal analogue of \\cite{CTZ} in that context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-02T20:48:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35P99",
      "58J51"
    ],
    "keywords": [
      "quantum ergodicity",
      "cross sections",
      "quantum flux norm",
      "second microlocal analogue",
      "non-degenerate energy surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}