{
  "id": "math-ph/0312050",
  "version": "v1",
  "published": "2003-12-19T16:39:54.000Z",
  "updated": "2003-12-19T16:39:54.000Z",
  "title": "On the structure of the essential spectrum of the three-particle Schrödinger operators on a lattice",
  "authors": [
    "Sergio Albeverio",
    "Saidakhmat N. Lakaev",
    "Zakhriddin I. Muminov"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "A system of three quantum particles on the three-dimensional lattice $\\Z^3$ with arbitrary \"dispersion functions\" having non-compact support and interacting via short-range pair potentials is considered. The energy operators of the systems of the two-and three-particles on the lattice $\\Z^3$ in the coordinate and momentum representations are described as bounded self-adjoint operators on the corresponding Hilbert spaces. For all sufficiently small nonzero values of the two-particle quasi-momentum $k\\in (-\\pi,\\pi]^3$ the finiteness of the number of eigenvalues of the two-particle discrete Schr\\\"odinger operator $h_\\alpha(k)$ below the continuous spectrum is established. A location of the essential spectrum of the three-particle discrete Schr\\\"odinger operator $H(K),K\\in (-\\pi,\\pi]^3$ the three-particle quasi-momentum, by means of the spectrum of $h_\\alpha(k)$ is described. It is established that the essential spectrum of $H(K), K\\in (-\\pi,\\pi]^3$ consists of a finitely many bounded closed intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-19T16:39:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "35P20",
      "47N50"
    ],
    "keywords": [
      "three-particle schrödinger operators",
      "essential spectrum",
      "short-range pair potentials",
      "sufficiently small nonzero values",
      "three-particle quasi-momentum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.ph..12050A"
    }
  }
}