Precision Finite Difference Monodromy Matrix
While at the University of California, Berkeley, I developed a new method for calculating the monodromy matrix. The monodromy (or stability) matrix is a quantity of central importance in many semiclassical theories; it is required to calculate the semiclassical prefactor, which helps capture many quantum effects in semiclassical calculations. Calculating it is one of the most computationally difficult parts of many semiclassical calculations.
I combined an idea from Grünwald, Dellago, and Geissler  with a naïve approach to the monodromy matrix to develop a method which was faster than the standard matrix-multiplication based methods to calculate the monodromy matrix, and more accurate that the naïve method which I improved upon.
Preliminary results from this project were presented at the 2010 ACS Spring Meeting in San Francisco. [Poster: 1.8MB]
 Michael Grünwald, Christoph Dellago, Phillip L. Geissler. J. Chem. Phys. 129, 194101 (2008).