Statistical dynamics of classical systems: a self-consistent field approach

We develop a self-consistent field theory for particle dynamics by extremizing the functional integral representation of a microscopic Langevin equation with respect to the collective fields. Although our approach is general, here we formulate it in the context of polymer dynamics to highlight satis...

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Bibliographic Details
Published in:The Journal of chemical physics 2014-06, Vol.140 (24), p.244907-244907
Main Authors: Grzetic, Douglas J, Wickham, Robert A, Shi, An-Chang
Format: Article
Language:English
Subjects:
Brownian motion
DENSITY
Dynamics
Field theory
INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
KINETICS
LANGEVIN EQUATION
MATHEMATICAL METHODS AND COMPUTING
MIXTURES
MONOMERS
PARTICLES
Phase separation
POLYMERS
SELF-CONSISTENT FIELD
TIME DEPENDENCE
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Summary:We develop a self-consistent field theory for particle dynamics by extremizing the functional integral representation of a microscopic Langevin equation with respect to the collective fields. Although our approach is general, here we formulate it in the context of polymer dynamics to highlight satisfying formal analogies with equilibrium self-consistent field theory. An exact treatment of the dynamics of a single chain in a mean force field emerges naturally via a functional Smoluchowski equation, while the time-dependent monomer density and mean force field are determined self-consistently. As a simple initial demonstration of the theory, leaving an application to polymer dynamics for future work, we examine the dynamics of trapped interacting Brownian particles. For binary particle mixtures, we observe the kinetics of phase separation.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.4884825