Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms
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2017-04-23
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We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schr"odinger equations, in the spirit of Tully's fewest switches surface hopping method. 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.
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Scholars@Duke
Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
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