Time Dependent Sampling and Path Sampling for Semiclassical IVRs

In an effort to reduce the number of trajectories required for semiclassical calculations, I tried including information about the time-evolved distribution in the Monte Carlo sampling for the double Herman-Kluk (DHK) semiclassical initial value representation (IVR). Historically, we have sampled using only the distribution at time zero. However, many trajectories initiated from those initial conditions end up unimportant at later times. Our idea was to reduce the contributing trajectories to those which are also important at the later time of interest. Unfortunately, this creates the problem that the initial conditions can be from disjoint regions of phase space.

I proposed a solution to that problem, based on using two Monte Carlo step sizes. I also compared sampling trajectory space by moving in phase space only at time zero with moving in phase space at any time, in a way analogous to transition path sampling. Results were presented at the 2011 Mini Stat Mech Meeting in Berkeley. [Poster: 7.3MB]