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Abstract: We develop efficient computational methods for oscillatory hyperbolic systems arising in non-adiabatic quantum dynamics involving band-crossing. Band-crossing is a quantum dynamical behavior that contributes to important physics and chemistry phenomena such as quantum tunneling, Berry connection, chemical reaction etc. In this talk, we will discuss our works in developing semiclassical methods for band-crossing in surface hopping. For such systems, which are hyperbolic but with oscillatory terms modeling non-adiabatic quantum transitions between different energy bands, we will introduce a nonlinear geometric optics method based "asymptotic-preserving" method that is accurate uniformly for all wave numbers, including the problem with random uncertain band gaps.
Bio: Shi Jin is the Director of Institute of Natural Sciences, and Chair Professor of Mathematics, at Shanghai Jiao Tong University. He also serves as a co-director of the Shanghai National Center for Applied Mathematics, director of Ministry of Education Key Lab on Scientific and Engineering Computing, and director of Shanghai Jiao Tong University Chongqing Artificial Intelligence Institute.
He is an inaugural Fellow of the American Mathematical Society (AMS) (2012), a Fellow of Society of Industrial and Applied Mathematics (SIAM) (2013), an inaugural Fellow of the Chinese Society of Industrial and Applied Mathematics (CSIAM) (2020), and an Invited Speaker at the International Congress of Mathematicians in 2018. In 2021 he was elected a Foreign Member of Academia Europaea and a Fellow of European Academy of Sciences. In 2024 he was awarded a Shanghai Natural Science Prize (first class).
His research interests include kinetic theory, hyperbolic conservation laws, quantum dynamics, uncertainty quantification, interacting particle systems, computational fluid dynamics, machine learning and quantum computing, etc.
