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Microscopic theory of brownian motion

Author

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  • Hynes, James T.
  • Kapral, Raymond
  • Weinberg, Michael

Abstract

In this article nonlinear Langevin equations for a brownian (B) particle are derived and analyzed. Attention is focussed on the role of nonlinear B particle momentum (P) modes (powers of P). The multimode Mori formalism is used to derive equations of motion for P(t) for different numbers n of modes included in the description. The well-known linear equation of Mori corresponds to the case n = 1. Friction kernels and random forces in these equations exhibit slow decay and mass ratio (λ) expansion anomalies due to mode coupling. The nonlinear Langevin equation obtained for a complete mode set (n = ∞) is free of these difficulties and is used to examine the first correction [O(λ4)] to standard O(λ2) results. Although no closed set of nonlinear Langevin equations exists at order λ4, a truncated set extends standard momentum correlation function predictions.

Suggested Citation

  • Hynes, James T. & Kapral, Raymond & Weinberg, Michael, 1975. "Microscopic theory of brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 81(4), pages 485-508.
    • Handle: RePEc:eee:phsmap:v:81:y:1975:i:4:p:485-508
    DOI: 10.1016/0378-4371(75)90071-0
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