{
  "id": "2102.02737",
  "version": "v1",
  "published": "2021-02-04T16:59:28.000Z",
  "updated": "2021-02-04T16:59:28.000Z",
  "title": "Insight of the Green's function as a defect state in a boundary value problem",
  "authors": [
    "Jose D. H. Rivero",
    "Li Ge"
  ],
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "A new perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a $\\delta$-function potential, the height of which depends on the Green's function itself. This approach is illustrated in one-dimensional and two-dimensional Helmholtz equation problems, with an emphasis on systems that are open and have a non-Hermitian potential. We then draw an analogy between the Green's function obtained this way and a chiral edge state circumventing a defect in a topological lattice, which shines light on the local minimum of the Green's function at the source position.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-04T16:59:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "greens function",
      "boundary value problem",
      "defect state",
      "two-dimensional helmholtz equation problems",
      "chiral edge state circumventing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}