{
  "id": "0705.0134",
  "version": "v2",
  "published": "2007-05-01T16:29:45.000Z",
  "updated": "2011-12-17T13:55:59.000Z",
  "title": "Semiclassical wave propagation for large times",
  "authors": [
    "Roman Schubert"
  ],
  "comment": "40 pages, 1 figure, This paper has been withdrawn by the author due to a gap in the proof of the dispersive estimates",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP",
    "nlin.CD"
  ],
  "abstract": "We study solutions of the time dependent Schr\\\"odinger equation on Riemannian manifolds with oscillatory initial conditions given by Lagrangian states. Semiclassical approximations describe these solutions for small h (where h is the semiclassical parameter), but their accuracy for large times is in general only understood up to the Ehrenfest time T ~ ln(1/h), and the most difficult case is the one where the underlying classical system is chaotic. We show that on surfaces of constant negative curvature semiclassical approximations remain accurate for times at least up to T ~ h^(-1/2) in the case that the Lagrangian state is associated with an unstable manifold of the geodesic flow.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-17T13:55:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semiclassical wave propagation",
      "large times",
      "curvature semiclassical approximations remain accurate",
      "lagrangian state",
      "negative curvature semiclassical approximations remain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0134S"
    }
  }
}