{
  "id": "2405.18988",
  "version": "v1",
  "published": "2024-05-29T11:07:46.000Z",
  "updated": "2024-05-29T11:07:46.000Z",
  "title": "Survival probability and position distribution of a run and tumble particle in $U(x)=α|x|$ potential with an absorbing boundary",
  "authors": [
    "Sujit Kumar Nath",
    "Sanjib Sabhapandit"
  ],
  "comment": "23 pages, 8 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the late time exponential decay of the survival probability $S_\\pm(t,a|x_0)\\sim e^{-\\theta(a)t}$, of a one-dimensional run and tumble particle starting from $x_0<a$ with an initial orientation $\\sigma(0)=\\pm 1$, under a confining potential $U(x)=\\alpha|x|$ with an absorbing boundary at $x=a>0$. We find that the decay rate $\\theta(a)$ of the survival probability has strong dependence on the location $a$ of the absorbing boundary, which undergoes a freezing transition at a critical value $a=a_c=(v_0-\\alpha)\\sqrt{v_0^2-\\alpha^2}/(2\\alpha\\gamma)$, where $v_0>\\alpha$ is the self-propulsion speed and $\\gamma$ is the tumbling rate of the particle. For $a>a_c$, the value of $\\theta(a)$ increases monotonically from zero, as $a$ decreases from infinity, till it attains the maximum value $\\theta(a_c)$ at $a=a_c$. For $0<a<a_c$, the value of $\\theta(a)$ freezes to the value $\\theta(a)=\\theta(a_c)$. We also obtain the propagator with the absorbing boundary condition at $x=a$. Our analytical results are supported by numerical simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-29T11:07:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "absorbing boundary",
      "survival probability",
      "tumble particle",
      "position distribution",
      "late time exponential decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}