DYNAMIC MEAN-FIELD MODELS WITH CORRELATED MODES

We discuss a generalized dynamic mean-field method combining the advan tages of explicit pair correlations and of configuration interaction. The approximate dynamical method, which we call time-dependent self-co nsistent-field configuration interaction (TDSCF2-CI), is constructed b y including N(N-1)/2 TDSCF2 configurations. In each configuration a gi ven pair of N coupled modes is directly (not in the mean-field approac h) correlated; the N(N-1)/2 configurations include all such choices of pairs. As such, it has both the usual advantages of TDSCF and improve ments due to some inclusion of correlations (exact results for any two -mode problem, improved descriptions of dynamical corrections, and gre ater accuracy). A three-mode model Hamiltonian is analyzed using five approximate treatments, i.e., the usual TDSCF, the three TDSCF2 forms, and the TDSCF2-CI one. The quantities for comparison with the exact r esults include the decay P(t) of the initial state, the time dependenc ies of the energies e (i) of individual modes, and the overlap S (t) o f the corresponding approximate wave function with the exact one. We f ind, indeed, that explicit inclusion of pair correlations improves the description of the quantum dynamics of the system.