Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?

Abstract

We aim to clarify confusions in the literature as to whether or not dynamical density functional theories for the one-body density of a classical Brownian fluid should contain a stochastic noise term. We point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified, depending on how the fluid one-body density is defined -- i.e. whether it is an ensemble averaged density distribution or a spatially and/or temporally coarse grained density distribution.

10 pages, 1 figure, to be submitted to Journal of Physics A: Mathematical and General

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• Dynamic Density Functional Theory of Fluids
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• Dynamical density functional theory and its application to spinodal decomposition
• On the controversy over the stochastic density functional equations
• mesoscopic approach to the slow dynamics of supercooled liquids and colloidal systems

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