  Non-equilibrium Green's Function (NGF) method is a powerful tool for studying
the evolution of quantum many-body systems. Different types of correlations can
be systematically incorporated within the formalism. The time evolution of the
single-particle Green's functions is described in terms of the Kadanoff-Baym
equations. The current work initially focuses on introducing the correlations
within infinite nuclear matter in one dimension and then in a finite system in
the NGF approach. Starting from the harmonic oscillator Hamiltonian, by
switching on adiabatically the mean-field and correlations simultaneously, a
correlated state with ground-state characteristics is arrived at within the NGF
method. Furthermore the use of cooling to for improving the adiabatic switching
is explored.
