{
  "id": "2212.02117",
  "version": "v1",
  "published": "2022-12-05T09:23:00.000Z",
  "updated": "2022-12-05T09:23:00.000Z",
  "title": "Pair correlation function of the one-dimensional Riesz gas",
  "authors": [
    "C. W. J. Beenakker"
  ],
  "comment": "7 pages, 1 figure",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A method from random-matrix theory is used to calculate the pair correlation function of a one-dimensional gas of $N\\gg 1$ classical particles with a power law repulsive interaction potential $u(x)\\propto |x|^{-s}$ (a socalled Riesz gas). An integral formula for the covariance of single-particle operators is obtained which generalizes known results in the limits $s\\rightarrow -1$ (Coulomb gas) and $s\\rightarrow 0$ (log-gas). As an application, we calculate the variance of the center of mass of the Riesz gas, which has a universal large-$N$ limit that does not depend on the shape of the confining potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-05T09:23:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pair correlation function",
      "one-dimensional riesz gas",
      "power law repulsive interaction potential",
      "random-matrix theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}