{
  "id": "1711.08474",
  "version": "v1",
  "published": "2017-11-22T19:13:00.000Z",
  "updated": "2017-11-22T19:13:00.000Z",
  "title": "Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension",
  "authors": [
    "Kanaya Malakar",
    "V. Jemseena",
    "Anupam Kundu",
    "K. Vijay Kumar",
    "Sanjib Sabhapandit",
    "Satya N. Majumdar",
    "S. Redner",
    "Abhishek Dhar"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-22T19:13:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "run-and-tumble particle",
      "first-passage properties",
      "relaxation",
      "one-dimension",
      "finite interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}