{
  "id": "1112.2607",
  "version": "v1",
  "published": "2011-12-12T16:26:41.000Z",
  "updated": "2011-12-12T16:26:41.000Z",
  "title": "Noise-induced drift in stochastic differential equations with arbitrary friction and diffusion in the Smoluchowski-Kramers limit",
  "authors": [
    "Scott Hottovy",
    "Giovanni Volpe",
    "Jan Wehr"
  ],
  "comment": "11 pages, 5 figures",
  "journal": "Journal of Statistical Physics, 2012, Volume 146, Number 4, Pages 762-773",
  "doi": "10.1007/s10955-012-0418-9",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP"
  ],
  "abstract": "We consider the dynamics of systems with arbitrary friction and diffusion. These include, as a special case, systems for which friction and diffusion are connected by Einstein fluctuation-dissipation relation, e.g. Brownian motion. We study the limit where friction effects dominate the inertia, i.e. where the mass goes to zero (Smoluchowski-Kramers limit). {Using the It\\^o stochastic integral convention,} we show that the limiting effective Langevin equations has different drift fields depending on the relation between friction and diffusion. {Alternatively, our results can be cast as different interpretations of stochastic integration in the limiting equation}, which can be parametrized by $\\alpha \\in \\mathbb{R}$. Interestingly, in addition to the classical It\\^o ($\\alpha=0$), Stratonovich ($\\alpha=0.5$) and anti-It\\^o ($\\alpha=1$) integrals, we show that position-dependent $\\alpha = \\alpha(x)$, and even stochastic integrals with $\\alpha \\notin [0,1]$ arise. Our findings are supported by numerical simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-12T16:26:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic differential equations",
      "arbitrary friction",
      "smoluchowski-kramers limit",
      "noise-induced drift",
      "friction effects dominate"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2012,
      "month": "Jan",
      "pages": 5
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JSP...tmp....5H"
    }
  }
}