{
  "annotation_id": "3364add9-f678-4050-9be5-52bff13a492b",
  "date_created": "2026-03-02T18:02:00.202000Z",
  "date_modified": "2026-03-02T18:02:00.202000Z",
  "file_hash": "3fe16b0d017770335249c21e65db343bced198f007ef3c8aefcaaee33df25a76",
  "private": false,
  "record": {
    "abstract": "The bounded one dimensional multibarrier potential shows signs of chaos,\nphase transition and a transmission probability of unity for certain values of\nits total length $L$ and the ratio $c$ of total interval to total width. Like\nthe infinite Kronig-Penney system, which is arranged along the whole spatial\nregion, the bounded multibarrier potential has a band-gap structure in its\nenergy spectrum. But unlike the Kronig-Penney system, in which the gaps\ndisappear for large energies, these gaps do not disappear for certain values of\n$L$ and $c$. The energy is discontinuous even in parts of the spectrum with no\ngaps at all. These results imply that the energy spectrum of the bounded\nmultibarrier system is singular.",
    "arxiv_id": "quant-ph/0306060",
    "authors": [
      "D. Bar"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10773-005-4686-x",
    "journal_ref": "IJTP, 44, 1281-1302 (2005)",
    "title": "The band-gap structure and the singular character of the bounded large   array of potential barriers",
    "url": "https://arxiv.org/abs/quant-ph/0306060"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8ef3bdd8-4cd0-42cb-a614-ac65d7b2d043",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}