{
  "id": "1703.10615",
  "version": "v1",
  "published": "2017-03-30T18:01:21.000Z",
  "updated": "2017-03-30T18:01:21.000Z",
  "title": "Quantum mechanical approach to stochastic resetting",
  "authors": [
    "Édgar Roldán",
    "Shamik Gupta"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the dynamics of overdamped Brownian particles diffusing in force fields and undergoing stochastic resetting to a given location with a generic {\\em space-dependent} rate of resetting. We introduce a novel quantum mechanical approach that allows to calculate in a systematic way analytical expressions for a variety of statistics of the dynamics, such as (i) the propagator prior to first reset; (ii) the distribution of the first-reset time, and, most interestingly, (iii) the spatial distribution of the particle at long times. A key to our accomplishment is the derivation of an equality relating the transition probability prior to first reset with the propagator of a suitable quantum mechanical problem. We apply our method to obtain {\\em exact} results for a number of representative and hitherto unexplored examples of resetting dynamics, including a case of energy-dependent resetting, thereby unveiling the nontrivial effects of resetting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-30T18:01:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic resetting",
      "first reset",
      "transition probability prior",
      "novel quantum mechanical approach",
      "systematic way analytical expressions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}