| Zhennan Zhou, Department of Mathematics, Duke University |
| Title: Asymptotically Compatible Schemes for Robust Discretization of Nonlocal Models |
| Abstract: We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schr\”odinger equations. The algorithm is asymptotically derived from the Schr\”odinger equation with rigorous approximation error analysis. The resulting algorithm can be viewed as a path integral stochastic representation of the semiclassical matrix Schr\”odinger 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 improved surface hopping algorithm with various numerical tests. |