Abstract for the talk on 24.03.2017 (11:00 h)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Jianfeng Lu (Duke University)
Frozen Gaussian approximation with surface hopping: a stochastic semiclassical algorithm for high dimensional Schroedinger equations
The numerical simulation of many-body quantum nuclear dynamics has been a long standing scientific challenge. Semiclassical methods, like ab initio molecular dynamics based on Born-Oppenheimer approximation, provide practical strategies to overcome the curse of dimensionality. The Born-Oppenheimer approximation breaks down however in the non-adiabatic regime. In this talk, we discuss some recent mathematical understanding and development of stochastic semiclassical methods for non-adiabatic quantum dynamics. In particular, we will present a rigorous surface hopping algorithm in the spirit of fewest switches surface hopping, based on a novel path integral representation of the semiclassical Schroedinger equations.