{
  "id": "2109.11101",
  "version": "v1",
  "published": "2021-09-23T01:51:28.000Z",
  "updated": "2021-09-23T01:51:28.000Z",
  "title": "First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry",
  "authors": [
    "Hanshuang Chen",
    "Feng Huang"
  ],
  "comment": "6 pages, 7 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the first passage properties of a Brownian particle diffusing freely inside a $d$-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean time to absorption (MTA) as functions of resetting rate $\\gamma$ and initial distance $r$ of the particle to the center of the sphere. We find that when $r>r_c$ there exists a nonzero optimal resetting rate $\\gamma_{{\\rm opt}}$ at which the MTA is a minimum, where $r_c=\\sqrt {d/\\left( {d + 4} \\right)} R$ and $R$ is the radius of sphere. As $r$ increases, $\\gamma_{{\\rm opt}}$ exhibits a continuous transition from zero to nonzero at $r=r_c$. Furthermore, we consider that the particle lies in between two two-dimensional or three-dimensional concentric spheres, and obtain the domain in which resetting expedites the MTA, which is $(R_1, r_{c_1}) \\cup (r_{c_2},R_2)$, with $R_1$ and $R_2$ being the radius of inner and outer spheres, respectively. Interestingly, when $R_1/R_2$ is less than a critical value, $\\gamma_{{\\rm opt}}$ exhibits a discontinuous transition at $r=r_{c_1}$; otherwise, such a transition is continuous. Whereas at $r=r_{c_2}$, $\\gamma_{{\\rm opt}}$ always shows a continuous transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-23T01:51:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic resetting",
      "diffusing particle",
      "bounded domains",
      "spherical symmetry",
      "particle diffusing freely inside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}