{
  "id": "2102.10603",
  "version": "v1",
  "published": "2021-02-21T13:38:53.000Z",
  "updated": "2021-02-21T13:38:53.000Z",
  "title": "Perturbation Theory for the Thermal Hamiltonian: 1D Case",
  "authors": [
    "Giuseppe De Nittis",
    "Vicente Lenz"
  ],
  "comment": "17 pages. Keywords: Thermal Hamiltonian, self-adjoint extensions, spectral theory, scattering theory",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "This work continues the study of the thermal Hamiltonian, initially proposed by J. M. Luttinger in 1964 as a model for the conduction of thermal currents in solids. The previous work [DL] contains a complete study of the \"free\" model in one spatial dimension along with a preliminary scattering result for convolution-type perturbations. This work complements the results obtained in [DL] by providing a detailed analysis of the perturbation theory for the one-dimensional thermal Hamiltonian. In more detail the following result are established: the regularity and decay properties for elements in the domain of the unperturbed thermal Hamiltonian; the determination of a class of self-adjoint and relatively compact perturbations of the thermal Hamiltonian; the proof of the existence and completeness of wave operators for a subclass of such potentials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-21T13:38:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "81Q05",
      "81Q15",
      "33C10"
    ],
    "keywords": [
      "perturbation theory",
      "1d case",
      "one-dimensional thermal hamiltonian",
      "thermal currents",
      "wave operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}