Microscopic theory of brownian motion. II. Nonlinear Langevin equations

Microscopic theory of brownian motion. II. Nonlinear Langevin equations

Publication Type:

Journal Article

Authors:

Hynes, J.T.; Kapral, R.; Weinberg, M.

Source:

Physica A: Statistical Mechanics and its Applications, Volume 81, Number 4, p.485-508 (1975)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-33645066601&doi=10.1016%2f0378-4371%2875%2990071-0&partnerID=40&md5=1e3bc12aab2adea2a98e80452eb22930

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. © 1975.