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      Noise-induced drift in stochastic differential equations with arbitrary friction and diffusion in the smoluchowski-kramers limit

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      Author(s)
      Hottovy, S.
      Volpe, G.
      Wehr, J.
      Date
      2012
      Source Title
      Journal of Statistical Physics
      Print ISSN
      0022-4715
      Electronic ISSN
      1572-9613
      Publisher
      Springer
      Volume
      146
      Issue
      4
      Pages
      762 - 773
      Language
      English
      Type
      Article
      Item Usage Stats
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      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 Itô 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 α∈ℝ. Interestingly, in addition to the classical Itô (α=0), Stratonovich (α=0. 5) and anti-Itô (α=1) integrals, we show that position-dependent α=α(x), and even stochastic integrals with α∉[0,1] arise. Our findings are supported by numerical simulations. © 2012 Springer Science+Business Media, LLC.
      Keywords
      Brownian motion
      Einstein mobility-diffusion relation
      Smoluchowski-Kramers approximation
      Stochastic differential equations
      Permalink
      http://hdl.handle.net/11693/21602
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s10955-012-0418-9
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      • Department of Physics 2397
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