{
  "id": "0711.2518",
  "version": "v1",
  "published": "2007-11-15T21:25:08.000Z",
  "updated": "2007-11-15T21:25:08.000Z",
  "title": "The spectrum of large powers of the Laplacian in bounded domains",
  "authors": [
    "E Katzav",
    "M Adda-Bedia"
  ],
  "comment": "13 pages, 2 figures",
  "journal": "J. Phys. A: Math. Theor. 41 (2008) 022002",
  "doi": "10.1088/1751-8113/41/2/022002",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "cond-mat.other",
    "cond-mat.soft",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-15T21:25:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded domain",
      "large powers",
      "3d laplacian problems",
      "exact results",
      "useful numerical approach valid"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2008,
      "month": "Jan",
      "volume": 41,
      "number": 2,
      "pages": "022002"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JPhA...41b2002K"
    }
  }
}