{
  "id": "1710.07525",
  "version": "v1",
  "published": "2017-10-20T13:27:10.000Z",
  "updated": "2017-10-20T13:27:10.000Z",
  "title": "Boundary triplets, tensor products and point contacts to reservoirs",
  "authors": [
    "A. A. Boitsev",
    "J. F. Brasche",
    "M. M. Malamud",
    "H. Neidhardt",
    "I. Yu. Popov"
  ],
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We consider symmetric operators of the form $S := A\\otimes I_{\\mathfrak T} + I_{\\mathfrak H} \\otimes T$ where $A$ is symmetric and $T = T^*$ is (in general) unbounded. Such operators naturally arise in problems of simulating point contacts to reservoirs. We construct a boundary triplet $\\Pi_S$ for $S^*$ preserving the tensor structure. The corresponding $\\gamma$-field and Weyl function are expressed by means of the $\\gamma$-field and Weyl function corresponding to the boundary triplet $\\Pi_A$ for $A^*$ and the spectral measure of $T$. Applications to 1-D Schr\\\"odinger and Dirac operators are given. A model of electron transport through a quantum dot assisted by cavity photons is proposed. In this model the boundary operator is chosen to be the well-known Jaynes-Cumming operator which is regarded as the Hamiltonian of the quantum dot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-20T13:27:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary triplet",
      "tensor products",
      "reservoirs",
      "weyl function",
      "quantum dot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}