Interacting distributed approximating functions for real-time quantum dynamics - Hoffman, David K.; Arnold, Mark; Zhu, Wei; Kouri, Donald J. (The Journal of chemical physics, 1993)
The distributed approximating function (DAF) approach to quantum real-time dynamics is generalized to include the effects of the potential. The ‘‘interacting’’ DAF (IDAF) is introduced as the identity for a certain class of functions that can be chosen to approximate as closely as desired any wave packet of interest. Free propagation of the IDAF yields the free propagator for the IDAF class in the coordinate representation, and substitution of this result into the Trotter form for the short-time full propagator, G(x,x′‖τ), yields the IDAF class full propagator, G(x,x′;{p}‖τ), in the coordinate representation. Here {p} denotes the set of parameters that determine the IDAF class. The IDAF class full propagator can be used to develop discretized path integral-based algorithms for real-time quantum dynamics. Use of G(x,x′;{p}‖τ) in the Feynman path integral formalism leads to a new result with interesting features compared to the standard path integral. Specifically, the IDAF class full propagator incorporates the classical force, and (1) automatically biases the dynamics toward the neighborhood of classical trajectories (but without relying on destructive and constructive interferences in that no recourse is made to stationary phase arguments), (2) automatically concentrates the wave packet in highly classical regions and attenuates the wave packet in highly nonclassical regions. Of the many possible IDAF-based algorithms two are presented as examples. One illustrates a Monte Carlo approach and the other a discretized matrix multiplication approach.