Non-markovian diffusion and Fokker-Planck equations for brownian oscillators

S. A. Adelman, B. J. Garrison

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16 Scopus citations


A generalized diffusion equation is derived from the Mori-Kubo generalized Langevin for a brownian oscillator subject to gaussian random but in general non-markovian noise. This equation involves a time-dependent diffusion function rather than a phenomenological diffusion constant. For long times the diffusion function approaches a constant for overdamped markovian oscillators; only in the limit of extreme overdamping is the phenomenological theory recovered. A previously derived generalized phase space Fokker-Planck equation for the brownian oscillator is shown to have incorrect short-time behaviour. The difficulty is traced to a transient systematic component of the Mori random force which is non-vanishing for classical lattices at 0 K. Fokker-Planck and diffusion equations for the brownian oscillator are derived from a generalized Langevin representation equivalent to, but distinct from, that of Mori and Kubo. The random force in this representation lacks the systematic transient component. The Fokker-Planck and diffusion equations obtained from this alternative Langevin representation are thus correct at all times.

Original languageEnglish (US)
Pages (from-to)1671-1681
Number of pages11
JournalMolecular Physics
Issue number6
StatePublished - Jun 1977

All Science Journal Classification (ASJC) codes

  • Biophysics
  • Molecular Biology
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry


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