Surface hopping algorithms are popular tools to study dynamics of the quantum-classical mixed systems. In this talk, we will present a surface hopping algorithm in diabatic representations, based on time dependent perturbation theory and semiclassical analysis. The algorithm can be viewed as a Monte Carlo sampling algorithm on the semiclassical path space for piecewise deterministic path with stochastic jumps between the energy surfaces. The algorithm is validated numerically and it shows good performance in both weak coupling and avoided crossing regimes.

This is joint work with Jianfeng Lu (Duke University).