{
  "annotation_id": "cb709e71-75f4-463b-a013-1da0f75d2e32",
  "date_created": "2026-03-02T18:01:39.256000Z",
  "date_modified": "2026-03-02T18:01:39.256000Z",
  "file_hash": "929f561985c43ea1ba57e3eef57198ffa72d992921ad1c84118b7b9c64ea187c",
  "private": false,
  "record": {
    "abstract": "We consider exact time-dependent analytic solutions to the Schr\\\"odinger\nequation for tunneling in one dimension with cut off wave initial conditions at\n$t=0$. We obtain that as soon as $t \\neq 0$ the transmitted probability density\nat any arbitrary distance rises instantaneously with time in a linear manner.\nUsing a simple model we find that the above nonlocal effect of the\ntime-dependent solution is suppressed by consideration of low-energy\nrelativistic effects. Hence at a distance $x_0$ from the potential the\nprobability density rises after a time $t_0=x_0/c$ restoring Einstein\ncausality. This implies that the tunneling time of a particle can never be\nzero.",
    "arxiv_id": "quant-ph/0006110",
    "authors": [
      "Gaston Garcia-Calderon",
      "Alberto Rubio",
      "Jorge Villavicencio"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.59.1758",
    "journal_ref": "Phys. Rev. A 59 (3) 1758 (1999)",
    "title": "Low-energy relativistic effects and nonlocality in time-dependent   tunneling",
    "url": "https://arxiv.org/abs/quant-ph/0006110"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "59c6148f-0a58-4668-a169-366ac56f754d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}