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

S. A. Adelman, Barbara Jane Garrison

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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
Volume33
Issue number6
DOIs
StatePublished - Jan 1 1977

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Fokker Planck equation
Fokker-Planck equation
oscillators
Morus
Noise

All Science Journal Classification (ASJC) codes

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

Cite this

Adelman, S. A. ; Garrison, Barbara Jane. / Non-markovian diffusion and Fokker-Planck equations for brownian oscillators. In: Molecular Physics. 1977 ; Vol. 33, No. 6. pp. 1671-1681.
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Non-markovian diffusion and Fokker-Planck equations for brownian oscillators. / Adelman, S. A.; Garrison, Barbara Jane.

In: Molecular Physics, Vol. 33, No. 6, 01.01.1977, p. 1671-1681.

Research output: Contribution to journalArticle

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