Surface hopping algorithms are popular tools to study dynamics of the
    quantum-classical mixed systems. In this paper, we propose 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.

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