{
  "id": "1805.07229",
  "version": "v1",
  "published": "2018-05-18T14:16:37.000Z",
  "updated": "2018-05-18T14:16:37.000Z",
  "title": "Spectral Theory of the Fermi Polaron",
  "authors": [
    "Marcel Griesemer",
    "Ulrich Linden"
  ],
  "comment": "36 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The Fermi polaron refers to a system of free fermions interacting with an impurity particle by means of two-body contact forces. Motivated by the physicists' approach to this system, the present article develops a general mathematical framework for defining many-body Hamiltonians with two-body contact interactions by means of a renormalization procedure. In the case of the Fermi polaron the well-known TMS Hamiltonians are shown to emerge. For the Fermi polaron in a two-dimensional box a novel variational principle, established within the general framework, links the low-lying eigenvalues of the system to the zero-modes of a Birman-Schwinger type operator. It allows us to show, e.g., that the \\emph{polaron}- and \\emph{molecule} energies, computed in the physical literature, are indeed upper bounds to the ground state energy of the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-18T14:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V70",
      "35P15"
    ],
    "keywords": [
      "spectral theory",
      "birman-schwinger type operator",
      "fermi polaron refers",
      "two-body contact forces",
      "novel variational principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}