Real-time computation of time-dependent quantum mechanical problems are presented for nuclear many-body problems. Quantum tunneling in nuclear fusion at low energy is described using a time-dependent wave packet. A real-time method of calculating strength functions using the time-dependent Schrödinger equation is utilized to properly treat the continuum boundary condition. To go beyond the few-body models, we resort to the density-functional theory. The nuclear mean-field models are briefly reviewed to illustrate its foundation and necessity of state dependence in effective interactions. This state dependence is successfully taken into account by the density dependence, leading to the energy density functional. Photoabsorption cross sections in 238 U are calculated with the real-time method for the time-dependent density-functional theory.
Real-time computation of time-dependent quantum mechanical problems are presented for nuclear many-body problems. Quantum tunneling in nuclear fusion at low energy is described using a time-dependent wave packet. A real-time method of calculating strength functions using the time-dependent Schrödinger equation is utilized to properly treat the continuum boundary condition. To go beyond the few-body models, we resort to the density-functional theory. The nuclear mean-field models are briefly reviewed to illustrate its foundation and necessity of state dependence in effective interactions. This state dependence is successfully taken into account by the density dependence, leading to the energy density functional. Photoabsorption cross sections in 238 U are calculated with the real-time method for the time-dependent density-functional theory.
Abstract. Using the time-dependent theory of quantum mechanics, we investigate nuclear electric dipole responses. The time evolution of a wave function is explicitly calculated in the coordinatespace representation. The particle continuum is treated with the absorbing boundary condition. Calculated time-dependent quantities are transformed into those of familiar energy representation. We apply the method to a three-body model for 11 Li and to the mean-field model for 22 O, then discuss properties of E1 response. TIME-DEPENDENT METHOD FOR NUCLEAR RESPONSES Atomic nuclei exhibit a variety of responses to different experimental probes; Coulomb and nuclear excitations, spin- and isospin-dependent probes, high- and low-energy reactions. In order to investigate properties of these nuclear excitations, it is useful to study response function for a probe (external) operator of interest. Normally, these quantum many-body problems are theoretically studied using the energy representation, in which calculations are carried out by either diagonalizing the Hamiltonian matrices or solving differential equations with a fixed energy. These approaches are advantageous when we are interested in states within a limited energy range. However, when we calculate
A general method for a microscopic description of nuclear dynamical problems is discussed. The method is based on a functional integral representation for the many-body time evolution operator U(tf,ti). In the stationary phase limit, a time-dependent mean-field approximation for the matrix elements of U is obtained. Using standard procedures this allows for extraction of quantum mechanical information about bound states, tunneling, or scattering phenomena in a many-nucleon system. The approximation represents a natural generalization of the time-dependent Hartree-Fock method.NUCLEAR STRUCTURE, NUCLEAR REACTIONS derived mean-field approximation for matrix elements of $\mathrm{exp}(\ensuremath{-}iHt)$ from exact functional integral; discussed relation to static HF, TDHF, and scattering calculations.
Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.
Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the \boldsymbol{GW} 𝐆 𝐖 approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.
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.
Quantum tunneling in many-body systems is the subject of many experimental and theoretical studies in fields ranging from cold atoms to nuclear physics. However, theoretical description of quantum tunneling with strongly interacting particles, such as nucleons in atomic nuclei, remains a major challenge in quantum physics. An initial-value approach to tunneling accounting for the degrees of freedom of each interacting particle is highly desirable. Inspired by existing methods to describe instantons with periodic solutions in imaginary time, we investigate the possibility to use an initial value approach to describe tunneling at the mean-field level. Real-time and imaginary-time Hartree dynamics are compared to the exact solution in the case of two particles in a two-well potential. Whereas real-time evolutions exhibit a spurious self-trapping effect preventing tunneling in strongly interacting systems, the imaginary-time-dependent mean-field method predicts tunneling rates in excellent agreement with the exact solution. Being an initial-value method, it could be more suitable than approaches requiring periodic solutions to describe realistic systems such as heavy-ion fusion.