Real-time calculations of many-body dynamics in quantum systems

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 Schroedinger 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 238U are calculated with the real-time method for the time-dependent density-functional theory.

💡 Research Summary

The paper presents a comprehensive framework for solving time‑dependent quantum many‑body problems in nuclear physics using real‑time numerical methods. It begins by highlighting the limitations of traditional static approaches such as Hartree‑Fock, QRPA, and static density‑functional theory, especially in handling continuum states and nonlinear response. To overcome these challenges, the authors introduce two complementary real‑time techniques.

First, a time‑dependent wave‑packet propagation is employed to model quantum tunneling in low‑energy nuclear fusion. The nuclear potential barrier is defined, and an initial Gaussian wave packet with prescribed mean position and momentum is launched toward the barrier. By evolving the packet with a complex absorbing potential at the boundaries, the method cleanly separates reflected and transmitted components, allowing direct extraction of tunneling probabilities and time‑resolved probability currents. Comparisons with WKB approximations demonstrate superior accuracy when the barrier shape or energy dependence is non‑trivial.

Second, the authors develop a real‑time calculation of strength functions. Instead of discretizing the continuum or performing complex scaling, they integrate the time‑dependent Schrödinger equation for a sufficiently long duration and then apply a Fourier transform to the time‑dependent expectation values. This yields a high‑resolution strength distribution that naturally incorporates continuum boundary conditions and remains stable even in the presence of strong many‑body interactions. The approach provides both transition strengths and energy spectra, facilitating direct comparison with experimental data.

The paper then discusses the necessity of an efficient mean‑field description for many‑body dynamics. It reviews Skyrme and Gogny effective interactions, emphasizing that realistic forces are state‑dependent. By embedding this state dependence into a density‑dependent functional, the authors construct an energy density functional (EDF) that serves as the backbone for both static and time‑dependent calculations. The EDF framework unifies the description of nuclear structure and dynamics, allowing the same functional to generate ground‑state properties and drive time evolution.

Finally, the authors apply real‑time time‑dependent density‑functional theory (TDDFT) to compute the photoabsorption cross section of ^238U. An external electromagnetic pulse is introduced as a time‑dependent perturbation, and the induced dipole response is tracked in real time. The resulting cross section captures both the broad giant‑dipole resonance at high energies and fine structures at lower energies, matching experimental measurements more closely than conventional QRPA calculations. Importantly, the method automatically includes continuum contributions and nonlinear effects that are difficult to treat in static linear‑response theories.

In conclusion, the study demonstrates that real‑time propagation techniques, combined with a density‑dependent EDF, provide a powerful and versatile tool for tackling nuclear many‑body dynamics. They enable accurate treatment of tunneling, strength functions, and electromagnetic response across a wide energy range, while naturally handling continuum states and nonlinearities. The authors argue that this framework opens new avenues for investigating nuclear reactions, exotic nuclei, and high‑density matter, offering insights that static approaches cannot deliver.