Local propagating Gaussians:: flexible vs. frozen widths

Recently we presented a method for modeling a quantum system to a bath that explicitly correlates the system with the individual bath modes. We do this through representation of the bath by locally propagating Gaussians (LPG), which change in position and momentum but remain Gaussian in form. The explicit correlation of the system to the bath modes enters through the simultaneous use of a different Gaussian for each state (or grid point) of the system. In this work, we look at two possibilities for the LPG method. In the frozen LPG, the width of the Gaussians is kept constant. In the flexible LPG, we relax this condition and allow for the width to be both time dependent and complex. We present a comparative study of these two methods and compare them with both time-dependent self-consistent field calculations (TDSCF) and an exact quantum calculation. The two LPG methods, in comparison with TDSCF, more accurately describe the exact dynamics. The difference is especially noticeable in the case of weak coupling, where the averaging done in TDSCF is an oversimplification of the system.