{
  "id": "1605.08348",
  "version": "v1",
  "published": "2016-05-26T16:05:41.000Z",
  "updated": "2016-05-26T16:05:41.000Z",
  "title": "Existence of Ground State Eigenvalues for the Spin-Boson Model with Critical Infrared Divergence and Multiscale Analysis",
  "authors": [
    "Volker Bach",
    "Miguel Ballesteros",
    "Martin Könenberg",
    "Lars Menrath"
  ],
  "comment": "29 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A two-level atom coupled to the radiation field is studied. First principles in physics suggest that the coupling function, representing the interaction between the atom and the radiation field, behaves like $\\vert k \\vert^{- 1/2}$, as the photon momentum k tends to zero. Previous results on non-existence of ground state eigenvalues suggest that in the most general case binding does not occur in the spin-boson model, i.e., the minimal energy of the atom-photon system is not an eigenvalue of the energy operator. Hasler and Herbst have shown [12], however, that under the additional hypothesis that the coupling function be off-diagonal -which is customary to assume-binding does indeed occur. In this paper an alternative proof of binding in case of off-diagonal coupling is given, i.e., it is proven that, if the coupling function is off-diagonal, the ground state energy of the spin-boson model is an eigenvalue of the Hamiltonian. We develop a multiscale method that can be applied in the situation we study, identifying a new key symmetry operator which we use to demonstrate that the most singular terms appearing in the multiscale analysis vanish.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-26T16:05:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground state eigenvalues",
      "spin-boson model",
      "critical infrared divergence",
      "multiscale analysis",
      "coupling function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}