Path integral and semiclassical methods for quantum dynamics
Forward-backward semiclassical dynamics (FBSD) is a rigorous and efficient methodology for capturing quantum mechanical effects in the time evolution of condensed phase systems through classical trajectory information. Combined with a discretized path integral representation of the Boltzmann operator, this methodology has enabled the simulation of the dynamics of such fluids as para-hydrogen and helium across the normal-to-superfluid transition. The results of these calculations are in very good agreement with experimental results on diffusion coefficients and dynamic structure factors probed by neutron scattering. The FBSD simulations provide novel insights into the separate roles of quantum mechanical and quantum statistical effects on the dynamics of these fluids.
Accurate, fully quantum mechanical results for the short-time behavior of complex-time correlation functions of low-temperature fluids have been obtained using the pair product approximation to evaluate the complex-time propagator in a single step. These results provide useful benchmarks for assessing the accuracy of approximate propagation methods.
Finally, an iterative Monte Carlo (IMC) methodology appears to overcome the sign problem associated with path integral calculations. By evaluating the discretized path integral expression iteratively on a grid selected by a Monte Carlo procedure. Both the grid points and the summations performed in each iteration utilize importance sampling, leading to favorable scaling with the number of particles, while the stepwise evaluation of the integrals circumvents the exponential growth of statistical error with time.