The basic concepts and recent developments in the time-dependent density-functional theory (TDDFT) for describing nuclear dynamics at low energy are presented. The symmetry breaking is inherent in nuclear energy density functionals, which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in the description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, the quantum fluctuations associated with slow collective motions are explicitly treated assuming that time evolution of densities is determined by a few collective coordinates and momenta. The concept of collective submanifold is introduced in the phase space associated with the TDDFT and used to quantize the collective dynamics. Selected applications are presented to demonstrate the usefulness and quality of the new approaches. Finally, conceptual differences between nuclear and electronic TDDFT are discussed, with some recent applications to studies of electron dynamics in the linear response and under a strong laser field.

We present a first-principles calculation for an optical dielectric breakdown in a diamond, which is induced by an intense laser field. We employ the time-dependent density-functional theory by solving the time-dependent Kohn–Sham equation in real time and real space. For low intensities, the ionization agrees well with the Keldysh formula. The calculation shows a qualitative change of electron dynamics as the laser intensity increases, from dielectric screening at low intensities to optical breakdown at and above $7\times {10}^{14}\text{W}/{\text{cm}}^2$. Following the pulse, the electrons excited into the conduction band exhibit a coherent plasma oscillation that persists for tens of femtoseconds.

We propose a practical method for solving the random-phase approximation (RPA) in the self-consistent Hartree-Fock (HF) and density-functional theory. The method is based on numerical evaluation of the residual interactions utilizing the finite amplitude of single-particle wave functions. The method only requires calculations of the single-particle Hamiltonian constructed with independent bra and ket states. Using the present method, the RPA calculation becomes possible with a little extension of a numerical code of the static HF calculation. We demonstrate the usefulness and accuracy of the present method by performing test calculations for isoscalar responses in deformed ${}^{20}\mathrm{Ne}$.

We present simple equations for a canonical-basis (Cb) formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the Cb. The Cb formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasiparticle random-phase approximation with Skyrme functionals. We show systematic studies of E1 strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, which include the neutron excess, the separation energy, the neutron-shell effects, the deformation, and the pairing.

We present the finite amplitude method (FAM), originally proposed in Ref. [17], for superfluid systems. A Hartree-Fock-Bogoliubov code may be transformed into a code of the quasiparticle-random-phase approximation (QRPA) with simple modifications. This technique has advantages over the conventional QRPA calculations, such as coding feasibility and computational cost. We perform the fully self-consistent linear-response calculation for the spherical neutron-rich nucleus ${}^{174}$Sn, modifying the hfbrad code, to demonstrate the accuracy, feasibility, and usefulness of the FAM.