{
  "id": "2202.00944",
  "version": "v1",
  "published": "2022-02-02T10:37:39.000Z",
  "updated": "2022-02-02T10:37:39.000Z",
  "title": "Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph",
  "authors": [
    "Emilia Blåsten",
    "Pavel Exner",
    "Hiroshi Isozaki",
    "Matti Lassas",
    "Jinpeng Lu"
  ],
  "comment": "36 pages, 4 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We consider the inverse scattering problems for two types of Schr\\\"odinger operators on locally perturbed periodic lattices. For the discrete Hamiltonian, the knowledge of the S-matrix for all energies determines the graph structure and the coefficients of the Hamiltonian. For locally perturbed equilateral metric graphs, the knowledge of the S-matrix for all energies determines the graph structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-02T10:37:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81U40",
      "47A40"
    ],
    "keywords": [
      "locally perturbed lattices",
      "discrete hamiltonian",
      "inverse problems",
      "quantum graph",
      "graph structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}