{
  "id": "2109.15026",
  "version": "v2",
  "published": "2021-09-30T11:50:59.000Z",
  "updated": "2022-05-16T12:19:35.000Z",
  "title": "Gap Statistics for Confined Particles with Power-Law Interactions",
  "authors": [
    "Saikat Santra",
    "Jitendra Kethepalli",
    "Sanaa Agarwal",
    "Abhishek Dhar",
    "Manas Kulkarni",
    "Anupam Kundu"
  ],
  "comment": "13 pages, 11 figures",
  "journal": "@article{year = 2022, month = {apr}, journal = {Physical Review Letters},Phys. Rev. Lett. 128, 170603}",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.quant-gas",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the $N$ particle classical Riesz gas confined in a one-dimensional external harmonic potential with power law interaction of the form $1/r^k$ where $r$ is the separation between particles. As special limits it contains several systems such as Dyson's log-gas ($k\\to 0^+$), Calogero-Moser model ($k=2$), 1d one component plasma ($k=-1$) and the hard-rod gas ($k\\to \\infty$). Despite its growing importance, only large-$N$ field theory and average density profile are known for general $k$. In this Letter, we study the fluctuations in the system by looking at the statistics of the gap between successive particles. This quantity is analogous to the well-known level spacing statistics which is ubiquitous in several branches of physics. We show that the variance goes as $N^{-b_k}$ and we find the $k$ dependence of $b_k$ via direct Monte Carlo simulations. We provide supporting arguments based on microscopic Hessian calculation and a quadratic field theory approach. We compute the gap distribution and study its system size scaling. Except in the range $-1<k<0$, we find scaling for all $k>-2$ with both Gaussian and non-Gaussian scaling forms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-05-16T12:19:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power-law interactions",
      "gap statistics",
      "confined particles",
      "one-dimensional external harmonic potential",
      "direct monte carlo simulations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}