ASTDLDA is a simplification of ASTDLDA in which the ensemble of propagated « pure » (in statistical physics terms) mean field states is replaced by one single « mixed » directly integrating correlations. The reduction implies a single associated mean field and thus loss of mean field fluctutaions but gain of the (costly) propagation of the various mean fields. Correlations are computed « a la STDLDA » by reconstituting occasionally an instantaneous STDLDA ensemble. This implies representing the mixed state by an ensemble of pure states for computing correlations which in particular allows to reconstruct many-body density matrices at any order, just as in STDLDA.
Note that in the text below, TDHF is used in place of TDLDA. The use of TDHF here stems from the nuclear physics origin of the theory. This does not implies that the underlying mean field theory should necessarily be TDHF in the sense of electronic systems. Any time-dependent mean field theory, effective or not, such as in particular the Time-Dependent Local Approximation (TDLDA) of Time-Dependent Density Functional Theory (TDDFT) can provide the basis for constructing STDHF.
