{
  "annotation_id": "528bfe36-9325-4327-8a23-62ca0b759c73",
  "date_created": "2026-03-02T18:02:40.979000Z",
  "date_modified": "2026-03-02T18:02:40.979000Z",
  "file_hash": "bb517ec5244d4b443256c555185132fd3fb78c369dab685fb0db9a64f749fdc7",
  "private": false,
  "record": {
    "abstract": "A one-dimensional discrete Stark Hamiltonian with a continuous electric field\nis constructed by extension theory methods. In absence of the impurities the\nmodel is proved to be exactly solvable, the spectrum is shown to be simple,\ncontinuous, filling the real axis; the eigenfunctions, the resolvent and the\nspectral measure are constructed explicitly. For this (unperturbed) system the\nresonance spectrum is shown to be empty. The model considering impurity in a\nsingle node is also constructed using the operator extension theory methods.\nThe spectral analysis is performed and the dispersion equation for the\nresolvent singularities is obtained. The resonance spectrum is shown to contain\ninfinite discrete set of resonances. One-to-one correspondence of the\nconstructed Hamiltonian to some Lee-Friedrichs model is established.",
    "arxiv_id": "quant-ph/9707050",
    "authors": [
      "L. A. Dmitrieva",
      "Yu. A. Kuperin",
      "Yu. B. Melnikov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/30/9/019",
    "title": "One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by   Impurities",
    "url": "https://arxiv.org/abs/quant-ph/9707050"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e968cf0a-b65b-40ed-812d-89337c5215eb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}