{
  "annotation_id": "b45059c8-9839-44d6-91ca-6c0491de1e99",
  "date_created": "2026-03-02T18:01:42.250000Z",
  "date_modified": "2026-03-02T18:01:42.250000Z",
  "file_hash": "cf00369b8f48a55e7f5fdadefdc4407953e5577b618620c469c06b479ebf90a6",
  "private": false,
  "record": {
    "abstract": "When an ion confined in a linear ion trap interacts with a coherent laser\nfield, the internal degrees of freedom, related to the electron transitions,\ncouple to the vibrational degree of freedom of the ion. As a result of this\ninteraction, quantum dynamics of the vibrational degree of freedom becomes\ncomplicated, and in some ranges of parameters even chaotic. We analyze the\nvibrational ion dynamics using a formal analogy with the solid-state problem of\nelectron localization. In particular, we show how the resonant approximation\nused in analysis of the ion dynamics, leads to a transition from a\ntwo-dimensional (2D) to a one-dimensional problem (1D) of electron\nlocalization. The localization length in the solid-state problem is estimated\nin cases of weak and strong interaction between the cites of the 2D cell by\nusing the methods of resonance perturbation theory, common in analysis of 1D\ntime-dependent dynamical systems.",
    "arxiv_id": "quant-ph/0012098",
    "authors": [
      "G. P. Berman",
      "A. R. Bishop",
      "D. F. V. James",
      "R. J. Hughes",
      "D. I. Kamenev"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.64.053406",
    "title": "Dynamical Stability of an Ion in a Linear Trap as a Solid-State Problem   of Electron Localization",
    "url": "https://arxiv.org/abs/quant-ph/0012098"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dd1da62e-5378-47ab-982d-6dc3f32d3dde",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}