报告摘要

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.

报告人简介

Prof. Jin is currently the Dean of the Institute of Natural Sciences and Chair Professor at the School of Mathematics at Shanghai Jiao Tong University. He also serves as Co-Director of the Shanghai Center for Applied Mathematics and Dean of the Chongqing Institute for Artificial Intelligence Research at Shanghai Jiao Tong University. He is a Fellow of the American Mathematical Society, a Fellow of the Society for Industrial and Applied Mathematics, an invited speaker at the 2018 International Congress of Mathematicians, and was elected as a Foreign Member of Academia Europaea and a Member of European Academy of Sciences in 2021. His research interests include scientific computing, kinetic theory, multiscale computing, computational fluid dynamics, uncertainty quantification, machine learning and quantum computing.