Real-time Kadanoff-Baym approach to nuclear response functions
  Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Green's functions in real time. Of particular interest is the effect of correlations. The system is therefore initially time-evolved with a collision term calculated in a direct Born approximation as well as with full (RPA) ring-summation until fully correlated. An external time-dependent potential is then applied. The ensuing density fluctuations are recorded to calculate the density response. This method was previously used by Kwong and Bonitz for studying plasma oscillations in a correlated electron gas. The energy-weighted sum-rule for the response function is guaranteed by using conserving self-energy insertions as the method then generates the full vertex-functions. These can alternatively be calculated by solving a Bethe -Salpeter equation as done in some previous works. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while $2^{nd}$ order self-energies are calculated using a particle-hole two-body effective (or 'residual') interaction given by a gaussian \it local \rm potential. We present numerical results for the response function $S(\omega,q_0)$ for $q_0=0.2,0.4$ and $0.8 {\rm fm}^{-1}$. Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included, the 'HF+RPA' approximation. We briefly discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Sj\"oberg and followers using methods developped by Babu and Brown, with special emphasis on the 'induced' interaction. 
H. S. K\"ohler and N. H. Kwong
nucl-th