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(λ 4)] to standard O(λ 2) results. Although no closed set of nonlinear Langevin equations exists at order λ 4, a truncated set extends standard momentum correlation function predictions.
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