{
  "annotation_id": "47b61945-3e3a-441e-85ac-1bbbafa3fa6a",
  "date_created": "2026-03-02T18:01:45.457000Z",
  "date_modified": "2026-03-02T18:01:45.457000Z",
  "file_hash": "343f338ae8ea14b247df8162a22286effe32e8af554c22c9446dad9521d87dfe",
  "private": false,
  "record": {
    "abstract": "We discuss the energy level splitting $\\Delta\\epsilon$ due to quantum\ntunneling between congruent tori in phase space. In analytic cases, it is well\nknown that $\\Delta\\epsilon$ decays faster than power of $\\hbar$ in the\nsemi-classical limit. This is not true in non-smooth cases, specifically, when\nthe tori are connected by line on which the Hamiltonian is not smooth. Under\nthe assumption that the non-smoothness depends only upon the x- or\np-coordinate, the leading term in the semi-classical expansion of\n$\\Delta\\epsilon$ is derived, which shows that $\\Delta \\epsilon$ decays as\n$\\hbar^{k+1}$ when $\\hbar\\to 0$ with k being the order of non-smoothness.",
    "arxiv_id": "quant-ph/0110126",
    "authors": [
      "Z. Q. Bai"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/35/8/307",
    "journal_ref": "J.Phys.A: Math. Gen. 35(2002)1895 (fwd)",
    "title": "Power-Law Energy Splitting Generated By Tunneling Between Non-smooth   Tori",
    "url": "https://arxiv.org/abs/quant-ph/0110126"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9da41149-7037-4912-a0d6-326f341a742c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}