{
  "id": "1503.08072",
  "version": "v1",
  "published": "2015-03-27T13:39:56.000Z",
  "updated": "2015-03-27T13:39:56.000Z",
  "title": "First-Passage of a Brownian Particle - Escape from a Bounded Potential",
  "authors": [
    "Markus Nyberg",
    "Tobias Ambjörnsson",
    "Ludvig Lizana"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Many different processes depend on the first crossing of a boundary. For example, the time it takes for a protein find its target site on DNA, and the waiting time until a neurone starts firing. Motivated by the lack of tools accessible for computing first passage time densities (FPDTs) for general potentials, we propose a new method based on the Independent Interval Approximation (IIA). We generalise the IIA framework to non-smooth Brownian processes and derive a closed form expression for the FPDT in Laplace space for arbitrary boundary and starting point in one dimension. We apply our results to a Brownian particle in a harmonic potential and we find good agreement with Langevin dynamics simulations for one and two boundaries. We anticipate that our results will have a wide applicability an a number of escape problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-27T13:39:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian particle",
      "bounded potential",
      "first-passage",
      "computing first passage time densities",
      "independent interval approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}