Predicting the organization and dynamics of neutrons and protons within atomic nuclei is a significant scientific challenge, crucial for designing future nuclear technologies and addressing fundamental questions such as the origin of heavy atoms in our universe. In this context, CEA, DAM, DIF develops theoretical approaches to simulate the dynamics of the elementary constituents of atomic nuclei. The equations of motion, derived within the framework of quantum mechanics, are solved on our supercomputers. The 2010s saw the rise of the time-dependent density functional theory (TDDFT) approach for tackling this problem. While TDDFT has provided groundbreaking insights into phenomena such as giant resonances observed in atomic nuclei and nuclear fission, this approximation has intrinsic limitations. This PhD project aims to develop and explore 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. 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.