Department of Physics, Society of Physics Students, Queens Campus

Time dependent density functional theory (TDDFT) is one of the useful tools for the study of the dynamic behavior of correlated electronic systems under the influence of external potentials. The success of this formally exact theory practically relies on approximations for the exchange-correlation potential which is a complicated non-local functional of the co-ordinate density. Adiabatic local approximations have been proposed and employed in several pioneering works of this field . However these approximations were found to suffer from mathematical inconsistencies and general applicability demands especially in the regime of strong field dynamics. We explore the regions where the theory faces challenges, and try to answer some of them via the insights from the many electron model systems. We want to answer the challenges the theory is facing currently by exploring the phase-space and semi-classical methods. The evolution scheme of the 1RDM (first order reduced density matrix) contains second-order reduced density matrix (2RDM), which has to be truncated in terms of 1RDMs. Any non-correlated approximations (Hartree-Fock) for 2RDM would fail to capture the natural occupations of the system. We show that by applying the quasi-classical and semi-classical approximations one can capture the natural occupations of the excited systems.