{
  "annotation_id": "2c7ffef5-34bb-4bae-83ee-bdd240d5dfd4",
  "date_created": "2026-03-02T18:02:45.077000Z",
  "date_modified": "2026-03-02T18:02:45.077000Z",
  "file_hash": "49d791f8867fe769f3b757854164bb2fd365a79e034907ba611a524ca77576bf",
  "private": false,
  "record": {
    "abstract": "We examine the effect of nonlinearity at a level crossing on the probability\nfor nonadiabatic transitions $P$. By using the Dykhne-Davis-Pechukas formula,\nwe derive simple analytic estimates for $P$ for two types of nonlinear\ncrossings. In the first type, the nonlinearity in the detuning appears as a\n{\\it perturbative} correction to the dominant linear time dependence. Then\nappreciable deviations from the Landau-Zener probability $P_{LZ}$ are found to\nappear for large couplings only, when $P$ is very small; this explains why the\nLandau-Zener model is often seen to provide more accurate results than\nexpected. In the second type of nonlinearity, called {\\it essential}\nnonlinearity, the detuning is proportional to an odd power of time. Then the\nnonadiabatic probability $P$ is qualitatively and quantitatively different from\n$P_{LZ}$ because on the one hand, it vanishes in an oscillatory manner as the\ncoupling increases, and on the other, it is much larger than $P_{LZ}$. We\nsuggest an experimental situation when this deviation can be observed.",
    "arxiv_id": "quant-ph/9811065",
    "authors": [
      "N. V. Vitanov",
      "K. -A. Suominen"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.59.4580",
    "title": "Nonlinear level crossing models",
    "url": "https://arxiv.org/abs/quant-ph/9811065"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0903aead-a694-4c1b-9013-f705b8e9efc7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}