{
  "id": "2002.10382",
  "version": "v1",
  "published": "2020-02-24T17:16:39.000Z",
  "updated": "2020-02-24T17:16:39.000Z",
  "title": "Spectral Theory of the Thermal Hamiltonian: 1D Case",
  "authors": [
    "Giuseppe De Nittis",
    "Vicente Lenz"
  ],
  "comment": "43 pages. Keywords: Thermal Hamiltonian, self-adjoint extensions, spectral theory, scattering theory",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "In 1964 J. M. Luttinger introduced a model for the quantum thermal transport. In this paper we study the spectral theory of the Hamiltonian operator associated to the Luttinger's model, with a special focus at the one-dimensional case. It is shown that the (so called) thermal Hamiltonian has a one-parameter family of self-adjoint extensions and the spectrum, the time-propagator group and the Green function are explicitly computed. Moreover, the scattering by convolution-type potentials is analyzed. Finally, also the associated classical problem is completely solved, thus providing a comparison between classical and quantum behavior. This article aims to be a first contribution in the construction of a complete theory for the thermal Hamiltonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-24T17:16:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "81Q05",
      "81Q15",
      "33C10"
    ],
    "keywords": [
      "thermal hamiltonian",
      "spectral theory",
      "1d case",
      "quantum thermal transport",
      "complete theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}