报告题目：Variationally evolving Gaussian wave packets
报告时间：2019年8月27日（周二）下午16: 00-17: 00
报告地点：雷丁楼N410室
报告人：Prof. Christian Lubich (University of Tübingen)
主持人：刘文军教授
报告摘要：The talk reviews Gaussian wave packets that evolve according to the Dirac--Frenkel time-dependent variational principle for the semi-classically scaled Schr\odinger equation. Old and new results on the approximation to the wave function are given, in particular an $L^2$ error bound that goes back to Hagedorn (1980) in a non-variational setting, and a new error bound for averages of observables with a Weyl symbol, which shows the double approximation order in the semiclassical scaling parameter in comparison with the norm estimate.
The variational equations of motion in Hagedorn's parametrization of the Gaussian are presented. They show a perfect quantum--classical correspondence and allow us to read off directly that the Ehrenfest time is determined by the Lyapunov exponent of the classical equations of motion.
A variational splitting integrator is formulated and its remarkable conservation and approximation properties are discussed. A new result shows that the integrator approximates averages of observables with the full order in the time stepsize, with an error constant that is uniform in the semiclassical parameter.
报告人简介：Christian Lubich教授是国际著名的数学家，尤其在数值分析、微分方程几何算法研究方面作出了杰出的贡献。2001年荣获SIAM Germund Dahlquist Prize，2018年荣获 SIAM Outstanding Paper Award，2018年在国际数学家大会（ICM）上作一小时特邀报告。目前担任《Foundations of Computational Mathematics》，《SIAMJournal of Numerical Analysis》，《Mathematics of Computation》，《IMA Journalof Numerical Analysis》，《Numerische Mathematik》等国际顶级期刊的编委。
数学与统计学院
2019年8月26日