{
  "id": "1610.06472",
  "version": "v1",
  "published": "2016-10-20T16:02:28.000Z",
  "updated": "2016-10-20T16:02:28.000Z",
  "title": "The Berry-Keating operator on a lattice",
  "authors": [
    "Jens Bolte",
    "Sebastian Egger",
    "Stefan Keppeler"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct and study a version of the Berry-Keating operator with a built-in truncation of the phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic oscillator, producing a difference operator on a finite, periodic lattice. We investigate the continuum and the infinite-volume limit of our model in conjunction with the semiclassical limit. Using semiclassical methods, we show that a specific combination of the limits leads to a logarithmic mean spectral density as it was anticipated by Berry and Keating.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-20T16:02:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "berry-keating operator",
      "logarithmic mean spectral density",
      "built-in truncation",
      "periodic lattice",
      "infinite-volume limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}