{
  "id": "1404.5232",
  "version": "v1",
  "published": "2014-04-21T16:15:17.000Z",
  "updated": "2014-04-21T16:15:17.000Z",
  "title": "Large fluctuations in diffusion-controlled absorption",
  "authors": [
    "Baruch Meerson",
    "S. Redner"
  ],
  "comment": "13 pages, 4 figures",
  "journal": "J. Stat. Mech. (2014) P08008",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Suppose that $N_0$ independently diffusing particles, each with diffusivity $D$, are initially released at $x=\\ell>0$ on the semi-infinite interval $0\\leq x<\\infty$ with an absorber at $x=0$. We determine the probability ${\\cal P}(N)$ that $N$ particles survive until time $t=T$. We also employ macroscopic fluctuation theory to find the most likely history of the system, conditional on there being exactly $N$ survivors at time $t=T$. Depending on the basic parameter $\\ell/\\sqrt{4DT}$, very different histories can contribute to the extreme cases of $N=N_0$ (all particles survive) and $N=0$ (no survivors). For large values of $\\ell/\\sqrt{4DT}$, the leading contribution to ${\\cal P}(N=0)$ comes from an effective point-like quasiparticle that contains all the $N_0$ particles and moves ballistically toward the absorber until absorption occurs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-21T16:15:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large fluctuations",
      "diffusion-controlled absorption",
      "employ macroscopic fluctuation theory",
      "semi-infinite interval",
      "particles survive"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2014/8/P08008",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2014,
      "month": "Aug",
      "volume": 2014,
      "number": 8,
      "pages": "08008"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JSMTE..08..008M"
    }
  }
}