The extension of Time Dependent Density Functional Theory (TDDFT) to superfluid systems is discussed in the context of nuclear reactions and large amplitude collective motion.
The formalism of density functional theory (DFT) can be easily extended to the time dependent case (TDDFT). However, while in the static case the theory is well established and is expected to be, at least in principle, an exact approach for the determination of energy and density profiles of inhomogeneous systems, the applicability of TDDFT to the investigation of dynamic phenomena (for example propagation of collective phenomena) is less obvious especially in the microscopic regime of large wave vectors. The purpose of this paper is to discuss some relevant questions concerning the structure, the ingredients and the applicability of TDDFT. Some emphasis will be also given to establish important connections between TDDFT and microscopic theories such as the Feynman theory for the elementary excitations of Bose superfluids.
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.. . . . . .
I describe the time-dependent superfluid local density approximation, which is an adiabatic extension of the density functional theory to superfluid Fermi systems and their real-time dynamics. This new theoretical framework has been used to describe several phenomena in cold atomic gases and nuclear collective motion: excitation of the Higgs modes in strongly interacting Fermi superfluids, generation of quantized vortices, crossing and reconnection of vortices, excitation of the superflow at velocities above the critical velocity, excitation of quantum shock waves and domain walls in the collisions of superfluid atomic clouds, and excitation of collective states in nuclei.