{
  "annotation_id": "39fb80f5-3ba9-4f94-b1dc-a6d24d1e68b8",
  "date_created": "2026-03-02T18:02:40.986000Z",
  "date_modified": "2026-03-02T18:02:40.986000Z",
  "file_hash": "749a01db27af28b9fce3e6701db8b9ec0a2f43648112cde856e60aad14e61bd8",
  "private": false,
  "record": {
    "abstract": "We discuss spectral properties of the Laplacian with multiple ($N$) point\ninteractions in two-dimensional bounded regions. A mathematically sound\nformulation for the problem is given within the framework of the self-adjoint\nextension of a symmetric (Hermitian) operator in functional analysis. The\neigenvalues of this system are obtained as the poles of a transition matrix\nwhich has size $N$. Closely examining a generic behavior of the eigenvalues of\nthe transition matrix as a function of the energy, we deduce the general\ncondition under which point interactions have a substantial effect on\nstatistical properties of the spectrum.",
    "arxiv_id": "quant-ph/9710005",
    "authors": [
      "T. Shigehara",
      "H. Mizoguchi",
      "T. Mishima",
      "Taksu Cheon"
    ],
    "categories": [
      "quant-ph",
      "chao-dyn",
      "cond-mat",
      "nlin.CD",
      "nucl-th"
    ],
    "title": "Spectral Properties of the Two-Dimensional Laplacian with a Finite   Number of Point Interactions",
    "url": "https://arxiv.org/abs/quant-ph/9710005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d14b3f0a-636c-4edc-9b25-68e08f3564c3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}