{
  "annotation_id": "ecd59d1a-3c76-4376-911f-7862e9cc1f28",
  "date_created": "2026-03-02T18:01:52.491000Z",
  "date_modified": "2026-03-02T18:01:52.491000Z",
  "file_hash": "6e7af6a39ab636b85ca69e5c9a77e6234c0fc45e536ac4493bbee23d2d1bf0b5",
  "private": false,
  "record": {
    "abstract": "We consider the Laplacian in a strip $\\mathbb{R}\\times (0,d)$ with the\nboundary condition which is Dirichlet except at the segment of a length $2a$ of\none of the boundaries where it is switched to Neumann. This operator is known\nto have a non-empty and simple discrete spectrum for any $a\u003e0$. There is a\nsequence $0\u003ca_1\u003ca_2\u003c...$ of critical values at which new eigenvalues emerge\nfrom the continuum when the Neumann window expands. We find the asymptotic\nbehavior of these eigenvalues around the thresholds showing that the gap is in\nthe leading order proportional to $(a-a_n)^2$ with an explicit coefficient\nexpressed in terms of the corresponding threshold-energy resonance\neigenfunction.",
    "arxiv_id": "quant-ph/0206113",
    "authors": [
      "D. Borisov",
      "P. Exner",
      "R. Gadyl\u0027shin"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.1519941",
    "journal_ref": "Journal of Mathematical Physics. 2002. V. 43. No. 12. P.\n  6265-6278.",
    "title": "Geometric coupling thresholds in a two-dimensional strip",
    "url": "https://arxiv.org/abs/quant-ph/0206113"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e55a666a-de98-42bb-bf7d-9c4b9b5cefcd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}