{
  "annotation_id": "7ceaafa8-6078-451d-9f9e-e95ede856e95",
  "date_created": "2026-03-02T18:01:45.527000Z",
  "date_modified": "2026-03-02T18:01:45.527000Z",
  "file_hash": "9033a8e425cfa2cb9d1b77d91bab60c5208dfc299f8c12d8dd7f689426379d3a",
  "private": false,
  "record": {
    "abstract": "We discuss the discrete spectrum of the Hamiltonian describing a\ntwo-dimensional quantum particle interacting with an infinite family of point\ninteractions. We suppose that the latter are arranged into a star-shaped graph\nwith N arms and a fixed spacing between the interaction sites. We prove that\nthe essential spectrum of this system is the same as that of the infinite\nstraight \"polymer\", but in addition there are isolated eigenvalues unless N=2\nand the graph is a straight line. We also show that the system has many\nstrongly bound states if at least one of the angles between the star arms is\nsmall enough. Examples of eigenfunctions and eigenvalues are computed\nnumerically.",
    "arxiv_id": "quant-ph/0106047",
    "authors": [
      "Pavel Exner",
      "Katerina Nemcova"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1088/0305-4470/34/38/306",
    "journal_ref": "J. Phys. A34 (2001), 7783-7794",
    "title": "Bound states in point-interaction star-graphs",
    "url": "https://arxiv.org/abs/quant-ph/0106047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6697f950-e9be-40d0-bc3f-341037753c78",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}