{
  "id": "1708.05422",
  "version": "v1",
  "published": "2017-08-17T19:58:12.000Z",
  "updated": "2017-08-17T19:58:12.000Z",
  "title": "Anomalous Dimension in a Two-Species Reaction-Diffusion System",
  "authors": [
    "Benjamin Vollmayr-Lee",
    "Jack Hanson",
    "R. Scott McIsaac",
    "Joshua D. Hellerick"
  ],
  "comment": "(9 pages, 7 figures)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study a two-species reaction-diffusion system with the reactions $A+A\\to (0, A)$ and $A+B\\to A$, with general diffusion constants $D_A$ and $D_B$. Previous studies showed that for dimensions $d\\leq 2$ the $B$ particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the $B$ particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling $C_{BB}(r,t) \\sim t^{\\phi}f(r/\\sqrt{t})$, where the exponent $\\phi$ results from the renormalization of the square of the field associated with the $B$ particles. We compute this exponent to first order in $\\epsilon=2-d$, a calculation that involves 61 Feynman diagrams, and also determine the logarithmic corrections at the upper critical dimension $d=2$. Finally, we determine the exponent $\\phi$ numerically utilizing a mapping to a four-walker problem for the special case of $A$ particle coalescence in one spatial dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-17T19:58:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-species reaction-diffusion system",
      "particle correlation function",
      "anomalous dimension resulting",
      "renormalization group methods",
      "particle density decays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}