Fully funded PhD at CEA. The scientific project aims at developing and exploring a novel theoretical approach to describe the collective motion of strongly correlated Fermions. The goal is to generalize the TDDFT framework to better describe observations such as the vibration damping in Fermions droplets. Building on initial work in this direction, the PhD candidate will derive the equations of motion for this new approach and implement them as an optimized library designed to leverage the computational power of CEA's supercomputers. The objective will be to assess how this new theoretical framework enhances predictions of the damping of giant resonances in atomic nuclei and the formation of fragments during nuclear fission.