{
  "id": "2006.13563",
  "version": "v1",
  "published": "2020-06-24T08:52:38.000Z",
  "updated": "2020-06-24T08:52:38.000Z",
  "title": "First-encounter time of two diffusing particles in confinement",
  "authors": [
    "F. Le Vot",
    "S. B. Yuste",
    "E. Abad",
    "D. S. Grebenkov"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "physics.chem-ph"
  ],
  "abstract": "We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we focus on two one-dimensional settings: a half-line and an interval. We first consider the case with equal particle diffusivities, for which exact results can be obtained for the survival probability and the associated first-encounter time density over the full time domain. We also evaluate the moments of the first-encounter time when they exist. We then turn to the case when the diffusivities are not equal, and focus on the long-time behavior of the survival probability. Our results highlight the great impact of boundary effects in diffusion-controlled kinetics even for simple one-dimensional settings, as well as the difficulty of obtaining analytic results as soon as translational invariance of such systems is broken.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-24T08:52:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diffusing particles",
      "confinement",
      "simple one-dimensional settings",
      "full time domain",
      "equal particle diffusivities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}