{
  "id": "1504.08283",
  "version": "v1",
  "published": "2015-04-30T15:57:22.000Z",
  "updated": "2015-04-30T15:57:22.000Z",
  "title": "Two interacting particles on the half-line",
  "authors": [
    "Joachim Kerner",
    "Tobias Mühlenbruch"
  ],
  "comment": "13 pages",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP",
    "math.SP"
  ],
  "abstract": "In the case of compact quantum graphs, many-particle models with singular two-particle interactions where introduced in [arXiv:1207.5648, arXiv:1112.4751] to provide a paradigm for further studies on many-particle quantum chaos. In this note, we discuss various aspects of such singular interactions in a two-particle system restricted to the half-line $\\mathbb{R}_+$. Among others, we give a description of the spectrum of the two-particle Hamiltonian and obtain upper bounds on the number of eigenstates below the essential spectrum. We also specify conditions under which there is at most one such eigenstate. As a final result, it is shown that the ground state is non-degenerate and decays exponentially as $\\sqrt{x^2+y^2} \\to \\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-30T15:57:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q35",
      "35J25",
      "35P15",
      "81Q10",
      "81V70"
    ],
    "keywords": [
      "interacting particles",
      "compact quantum graphs",
      "singular two-particle interactions",
      "many-particle quantum chaos",
      "many-particle models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}