{
  "id": "2206.03947",
  "version": "v1",
  "published": "2022-06-08T15:11:41.000Z",
  "updated": "2022-06-08T15:11:41.000Z",
  "title": "Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations",
  "authors": [
    "Dmytro Shapoval",
    "Viktoria Blavatska",
    "Maxym Dudka"
  ],
  "comment": "24 pages, 11 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We analyze the two-species reaction-diffusion system including trapping reaction $A + B \\to A$ as well as coagulation/annihilation reactions $A + A \\to (A,0)$ where particles of both species are performing L\\'evy flights with control parameter $0 < \\sigma < 2$, known to lead to superdiffusive behaviour. The density, as well as the correlation function for target particles $B$ in such systems, are known to scale with nontrivial universal exponents at space dimension $d \\leq d_{c}$. Applying the renormalization group formalism we calculate these exponents in a case of superdiffusion below the critical dimension $d_c=\\sigma$. The numerical simulations in one-dimensional case are performed as well. The quantitative estimates for the decay exponent of the density of survived particles $B$ are in good agreement with our analytical results. In particular, it is found that the surviving probability of the target particles in a superdiffusive regime is higher than that in a system with ordinary diffusion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-08T15:11:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "renormalization group treatment",
      "two-species reaction-superdiffusion system",
      "numerical simulations",
      "target particles",
      "two-species reaction-diffusion system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}