Derivation of dynamical density functional theory using the projection operator technique.

Area of Science:

• Theoretical physics
• Statistical mechanics
• Condensed matter theory

Background:

• Density functional theory (DFT) is a quantum mechanical method used to investigate the electronic structure of materials.
• The projection operator technique is a mathematical tool used to simplify complex quantum systems.
• Dynamical extensions of DFT are needed to describe time-dependent phenomena.

Purpose of the Study:

• To derive a general dynamical version of density functional theory.
• To introduce a generalized diffusion tensor within this framework.
• To connect the new theory to existing models for specific systems.

Main Methods:

• Utilizing a general theory of conjugate variables.
• Applying the projection operator technique.
• Deriving the generalized diffusion tensor via a Green-Kubo expression.

Main Results:

• A novel, generalized dynamical density functional theory was formulated.
• The theory incorporates a generalized diffusion tensor.
• The standard dynamical density functional theory was recovered for Brownian dynamics of dilute colloidal suspensions.

Conclusions:

• The developed dynamical density functional theory provides a more general framework for studying time-dependent systems.
• The generalized diffusion tensor is a key component for describing particle dynamics.
• This work bridges fundamental theory with applications in areas like colloidal science.