A Dynamic Density Functional Theory approach to Pattern Formation

Density functional theory (DFT), in both its classical and quantum formulations, presents a framework for determining the ground-state density of a given material through the variational minimization of a free energy functional. Using this framework, relevant energetic contributions can be accounted for self-consistently, and both microscopic and macroscopic degrees of freedom can be connected naturally. While DFT is traditionally used to determine equilibrium properties, one possible extension to model non-equilibrium systems is through the use of dynamic DFT (DDFT). DDFT builds upon the continuity equation within the Stokes limit, which includes nonlocal effects that capture the contributions of many-body correlations. Here, we propose a phenomenological DDFT model for the purpose of describing the emergence of pattern formation, that maintains both conservation laws and proper scalings in the high-frequency limit. Simulation results are presented and compared to experiment and other models for pattern formation.