Microscopic theory of brownian motion. III. The nonlinear Fokker-Planck equation

Microscopic theory of brownian motion. III. The nonlinear Fokker-Planck equation

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.509-521 (1975)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-49649133904&doi=10.1016%2f0378-4371%2875%2990072-2&partnerID=40&md5=d423833478bcdac69d363326e32c7cb9

Abstract:

The nonlinear Fokker-Planck equation for the momentum distribution of a brownian particle of mass M in a bath of particles of mass m is derived. The contribution to this equation arising from initial deviation from bath equilibrium is analysed. This contribution is free of slow M-dependent decays and with certain restrictions leads to an effective shift in the initial value of the B particle momentum. The nonlinear Fokker-Planck equation for an initial bath equilibrium state is analyzed in terms of its predictions for momentum relaxation and mode coupling effects. It is found that in addition to nonlinear renormalization of the type previously found for the momentum correlation function, mode coupling leads to long-lived memory of the initial momentum state. © 1975.