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

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.

[1]  J. Dhont.  Spinodal decomposition of colloids in the initial and intermediate stages , 1996 .

[2]  J. Zinn-Justin.  Quantum Field Theory and Critical Phenomena , 2002 .

[3]  Jerome Percus,et al.  Equilibrium state of a classical fluid of hard rods in an external field , 1976 .

[4]  T. Munakata.  A Dynamical Extension of the Desity Functional Theory , 1989 .

[5]  H. Risken.  The Fokker-Planck equation : methods of solution and applications , 1985 .

[6]  N. Goldenfeld.  Lectures On Phase Transitions And The Renormalization Group , 1972 .

[7]  H. Reiss,et al.  The role of fluctuations in both density functional and field theory of nanosystems. , 2004, The Journal of chemical physics.

[8]  R. Evans.  The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids , 1979 .

[9]  Dynamic density functional theory of fluids , 2000 .

[10]  Kyozi Kawasaki,et al.  Stochastic model of slow dynamics in supercooled liquids and dense colloidal suspensions , 1994 .

[11]  A. Archer,et al.  Dynamical density functional theory and its application to spinodal decomposition. , 2004, The Journal of chemical physics.

[12]  T. R. Kirkpatrick,et al.  Random solutions from a regular density functional Hamiltonian: a static and dynamical theory for the structural glass transition , 1989 .

[13]  A mesoscopic approach to the slow dynamics of supercooled liquids and colloidal systems , 2001, cond-mat/0109249.

[14]  H. Risken.  Fokker-Planck Equation , 1984 .

[15]  K. Kawasaki.  Microscopic Analyses of the Dynamical Density Functional Equation of Dense Fluids , 1998 .

[16]  D. Dean.  LETTER TO THE EDITOR: Langevin equation for the density of a system of interacting Langevin processes , 1996, cond-mat/9611104.