{
  "id": "2102.07232",
  "version": "v1",
  "published": "2021-02-14T20:07:39.000Z",
  "updated": "2021-02-14T20:07:39.000Z",
  "title": "Dynamical phase transition in the first-passage probability of a Brownian motion",
  "authors": [
    "Benjamin Besga",
    "Felix Faisant",
    "Artyom Petrosyan",
    "Sergio Ciliberto",
    "Satya N. Majumdar"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We study theoretically, experimentally and numerically the probability distribution $F(t_f|x_0,L)$ of the first passage times $t_f$ needed by a freely diffusing Brownian particle to reach a target at a distance $L$ from the initial position $x_0$, taken from a normalized distribution $(1/\\sigma)\\, g(x_0/\\sigma)$ of finite width $\\sigma$. We show the existence of a critical value $b_c$ of the parameter $b=L/\\sigma$, which determines the shape of $F(t_f|x_0,L)$. For $b>b_c$ the distribution $F(t_f|x_0,L)$ has a maximum and a minimum whereas for $b<b_c$ it is a monotonically decreasing function of $t_f$. This dynamical phase transition is generated by the presence of two characteristic times $\\sigma^2/D$ and $L^2/D$, where $D$ is the diffusion coefficient. The theoretical predictions are experimentally checked on a Brownian bead whose free diffusion is initialized by an optical trap which determines the initial distribution $g(x_0/\\sigma)$. The presence of the phase transition in 2d has also been numerically estimated using a Langevin dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-14T20:07:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamical phase transition",
      "first-passage probability",
      "brownian motion",
      "first passage times",
      "probability distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}