Precision finite difference monodromy matrix

The semiclassical initial value representation (SC-IVR) captures quantum dynamical effects by running many classical trajectories. However the most accurate versions of the SC-IVR require propagating additional information, called the “monodromy matrix,” which is the most expensive part of the simulation. I developed a new approach to calculate the monodromy matrix that was both efficient and general.

The most efficient approaches to calculate the monodromy matrix require specialized calculations in the underlying dynamics, which often aren’t directly available without significant programming effort. Approaches that don’t require this are more general. My method, the “precision finite difference (PFD) monodromy matrix”, is general and is more efficient than previously existing general approaches.