Surface hopping algorithms in quantum dynamics and thermal equilibrium sampling

摘要：           We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schrodinger equations.
                       The algorithm is asymptotically derived from the Schrodinger equation with rigorous approximation error analysis. The resulting a
                       lgorithm can be viewed as a path integral stochastic representation of the semiclassical matrix Schrodinger equations. Our results
                      provide mathematical understanding to and shed new light on the important class of surface hopping methods in theoretical and
                      computational chemistry. Also, I would like to report our recent progress on the path integral molecular dynamics with surface
                      hopping (PIMD-SH) for thermal equilibrium sampling of nonadiabatic systems, where a novel ring polymer representation for
                      multi-level quantum system is proposed for thermal average calculations.