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.. . . . . .
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.
A configuration-interaction time-dependent density functional theory (CI-TDDFT) for nuclear dynamics is developed. In this framework, the correlated nuclear many-body wave function is expanded in terms of time-dependent many-particle configurations built from a common set of orthonormal single-particle states. The equations of motion for both the expansion coefficients and the single-particle states are derived self-consistently using the Dirac-Frenkel time-dependent variational principle. This formulation extends conventional time-dependent density functional theory (TDDFT) by incorporating configuration mixing and beyond-mean-field correlations, while preserving energy and particle-number conservation. As an illustrative application, the method is implemented using the relativistic point-coupling functional PC-PK1 in the particle-hole channel and a monopole pairing interaction in the particle-particle channel, and is applied to the study of isoscalar giant monopole resonance in
58Ni and
60Ni. Numerical tests show that both the total energy and particle number are conserved, with relative deviations within
4×10−4 during the time evolution. Compared with conventional TDDFT, CI-TDDFT yields broader strength distributions for giant monopole resonances while keeping the main peak positions close to those from TDDFT. This broadening is associated with configuration mixing in the valence space and suggests a coupling of the monopole oscillation to additional collective degrees of freedom. These results demonstrate the potential of CI-TDDFT as a quantum, microscopic beyond-mean-field framework for nuclear dynamics.
Time-dependent density-functional theory (TDDFT) treats dynamical exchange and correlation (xc) via a single-particle potential,
Vxc(r,t), defined as a nonlocal functional of the density $n({\mathbf{r}}^{\ensuremath{'}},{t}^{\ensuremath{'}})$. The popular adiabatic local-density approximation (ALDA) for
Vxc(r,t) uses only densities at the same space-time point
(r,t). To go beyond the ALDA, two local approximations have been proposed based on quantum hydrodynamics and elasticity theory: (a) using the current as the basic variable (C-TDDFT) [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4847 (1997)], (b) working in a comoving Lagrangian reference frame (L-TDDFT) [I. V. Tokatly, Phys. Rev. B 71, 165105 (2005)]. In this paper we illustrate, compare, and analyze both nonadiabatic theories for simple time-dependent model densities in the linear and nonlinear regime, for a broad range of time and frequency scales. C- and L-TDDFT are identical in certain limits, but, in general, exhibit qualitative and quantitative differences in their respective treatment of elastic and dissipative electron dynamics. In situations where the electronic density rapidly undergoes large deformations, it is found that nonadiabatic effects can become significant, causing the ALDA to break down.