{
  "id": "2010.14237",
  "version": "v1",
  "published": "2020-10-27T12:14:20.000Z",
  "updated": "2020-10-27T12:14:20.000Z",
  "title": "Space-dependent diffusion with stochastic resetting: A first-passage study",
  "authors": [
    "Somrita Ray"
  ],
  "comment": "10 pages, 5 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We explore the effect of stochastic resetting on the first-passage properties of space-dependent diffusion in presence of a constant bias. In our analytically tractable model system, a particle diffusing in a linear potential $U(x)\\propto\\mu |x|$ with a spatially varying diffusion coefficient $D(x)=D_0|x|$ undergoes stochastic resetting, i.e., returns to its initial position $x_0$ at random intervals of time, with a constant rate $r$. Considering an absorbing boundary placed at $x_a<x_0$, we first derive an exact expression of the survival probability of the diffusing particle in the Laplace space and then explore its first-passage to the origin as a limiting case of that general result. In the limit $x_a\\to0$, we derive an exact analytic expression for the first-passage time distribution of the underlying process. Once resetting is introduced, the system is observed to exhibit a series of dynamical transitions in terms of a sole parameter, $\\nu=(1+\\mu D_0^{-1})$, that captures the interplay of the drift and the diffusion. Constructing a full phase diagram in terms of $\\nu$, we show that for $\\nu<0$, i.e., when the potential is strongly repulsive, the particle can never reach the origin. In contrast, for weakly repulsive or attractive potential ($\\nu>0$), it eventually reaches the origin. Resetting accelerates such first-passage when $\\nu<3$, but hinders its completion for $\\nu>3$. A resetting transition is therefore observed at $\\nu=3$, and we provide a comprehensive analysis of the same. The present study paves the way for an array of theoretical and experimental works that combine stochastic resetting with inhomogeneous diffusion in a conservative force-field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-27T12:14:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic resetting",
      "space-dependent diffusion",
      "first-passage study",
      "full phase diagram",
      "exact analytic expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}