Editing Dynamical density-functional theory

'''Dynamical Density functional theory''' is a set of theories in [[statistical mechanics]] that
extends [[equilibrium density functional theory | Density functional theory]] to
situations away from equilibrium. In the simplest case, only small deviations from equilibrium are
considered, so that linear response theory can be applied.

A simple approach in this line is to consider this evolution of the density field:

:<math> \frac{\partial\rho}{\partial t}=  - \mu \frac{\delta A}{\delta\rho}.</math>

In equilibrium, the left hand side vanishes and we are left with the usual density functional
expression. Away from it, an increase in the free energy ''A'' causes
a decrease in the density, mediated by the mobility coefficient <math>\mu</math>.

This sort of evolution will not satisfy conservation of the number of particles
(that is, the space integral of the density field), and is therefore termed ''non-conserved dynamics''. This can be valid in cases in which this field is in fact not conserved, such as the magnetization field in a model for magnets (such as the [[Ising model]]).

In other cases, for example with actual particles,
some evolution has to be postulated. For example, this evolution will conserve
the number of particles:

:<math> \frac{\partial\rho}{\partial t}=  - \nabla \mu \nabla \frac{\delta A}{\delta\rho}.</math>

The later sort of expressions are called ''non-conserved dynamics''.




==See also==
*[[Brownian dynamics]]


==Interesting reading==
*[http://dx.doi.org/10.1088/0953-8984/12/8A/356 Umberto Marini Bettolo Marconi and Pedro Tarazona "Dynamic density functional theory of fluids",  J. Phys.: Condens. Matter '''12''' A413(2000)]

[[category: Density-functional theory]]