5月22日，德国图宾根大学Christian Lubich教授受邀参加第五期线上“自然科学杰出演讲系列讲座”，以“Variationally evolving Gaussians revisited ”为题为海内外师生带来一场精彩纷呈的学术报告。本次学术报告由自然科学研究院院长金石教授主持，来自数学科学学院、物理与天文学院、致远学院以及海内外其他高校师生共同参会。
本次报告主要介绍如何利用variational Gaussian wave packet方法高效计算半经典的多粒子薛定谔方程。Lubich教授对这套方法的基本思想、与真实解的误差估计、波包中参数的演化方程以及如何高效数值实现做了细致的讲解。最后，Lubich教授与师生在线上展开热烈讨论。
嘉宾介绍： Christian Lubich，德国图宾根大学教授，时间依赖问题方面的专家，包括常微分方程和相关的演化积分方程。Christian Lubich教授与Ernst Hairer教授、Gerhard Wanner教授合著具有影响力的专著《几何数值积分》。Lubich教授近期的研究兴趣包括高维矩阵和张量微分方程的动力学低秩逼近，及其在量子动力学和等离子体物理学中的应用，高频振荡问题。例如半经典量子动力学和强磁场中的带电粒子动力学，波动方程的稳定数值内外耦合，以及诸如平均曲率流等几何演化方程的数值分析。Lubich教授是数值分析领域内顶级期刊的编委，也是Oberwolfach数学研究所科学委员会的成员。Lubich教授荣获“SIAM Dahlquist Prize”，并于2018年在里约热内卢举行的国际数学家大会上作大会报告。
On May 22, Christian Lubich, Professor of Numerical Mathematics at the University of Tuebingen (Germany) was invited to deliver the 5th “Distinguished Lecture in Natural Sciences” at INS. The lecture “Variationally evolving Gaussians revisited” has amazed teachers and students at home and abroad. This lecture was chaired by Professor Shi Jin, Director of the Institute of Natural Sciences. The teachers and students from the School of Mathematical Sciences, SJTU, the School of Physics and Astronomy, SJTU, Zhiyuan College, SJTU, and other domestic and overseas universities participated in the conference.
This talk mainly introduced how to use the method of variational Gaussian wave packet to efficiently calculate the semiclassical multi-particle Schroedinger equation. Prof.Lubich gave a detailed explanation of the basic idea of this method, the error estimate between the approximate and exact solution, the evolution equation of the parameters in the wave packet, and how to implement the numerical computation efficiently. Finally, Prof.Lubich had an in-depth discussion with teachers and students online.
Bio： Christian Lubich is Professor of Numerical Mathematics at the University of Tuebingen (Germany). He is an expert in the numerical analysis of time-dependent problems, whether ordinary or partial differential equations or related evolutionary integral equations. He is a coauthor, with Ernst Hairer and Gerhard Wanner, on an influential monograph on Geometric Numerical Integration. His recent research interests include dynamical low-rank approximation of high-dimensional matrix and tensor differential equations with applications to quantum dynamics and plasma physics, highly oscillatory problems such as quantum dynamics in the semiclassical regime and charged-particle dynamics in a strong magnetic field, stable numerical interior-exterior coupling of wave equations, and the numerical analysis of geometric evolution equations such as mean curvature flow. Professor Lubich is a member of the editorial boards of leading journals in numerical analysis and a member of the Scientific Committee of the Oberwolfach Mathematical Research Institute. He won a SIAM Dahlquist Prize, and gave a plenary lecture at the International Congress of Mathematicians in Rio de Janeiro in 2018 on “Dynamics, numerical analysis, and some geometry”.