Density functional approaches to collective phenomena in nuclei: Time-dependent density functional theory for perturbative and non-perturbative nuclear dynamics

We present the basic concepts and our recent developments in density functional approaches with Skyrme functionals for describing nuclear dynamics at low energy. Time-dependent density functional theory (TDDFT) is utilized for the exact linear response with an external perturbation. For a description of collective dynamics beyond the perturbative regime, we present a theory of a decoupled collective submanifold to describe a slow motion based on TDDFT. Selected applications are shown to demonstrate the quality of their performance and feasibility. The advantages and disadvantages of the numerical aspects are also discussed.