# Editing Dynamical density-functional theory

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'''Dynamical Density functional theory''' is a set of theories in [[statistical mechanics]] that | '''Dynamical Density functional theory''' is a set of theories in [[statistical mechanics]] that | ||

− | extends | + | extends [[equilibrium density functional theory | Density functional theory]] to |

− | situations away from | + | situations away from equilibrium. In the simplest case, only small deviations from equilibrium are |

− | considered, so that | + | considered, so that linear response theory can be applied. |

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

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

− | In equilibrium, the left hand side vanishes and | + | In equilibrium, the left hand side vanishes and we are left with the usual density functional |

− | expression. Away from it, an increase in the | + | expression. Away from it, an increase in the free energy ''A'' causes |

− | a decrease in the density, mediated by the | + | 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 | 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 | + | (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, | In other cases, for example with actual particles, | ||

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

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==See also== | ==See also== | ||

*[[Brownian dynamics]] | *[[Brownian dynamics]] | ||

− | + | ||

− | + | ||

==Interesting reading== | ==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", | + | *[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]] | [[category: Density-functional theory]] |