Frozen Gaussian approximation with surface hopping: a stochastic semiclassical algorithm for high dimensional
Schroedinger equations
Jianfeng Lu, Duke

Abstract:
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.