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Random Batch Methods for classical and quantum N-body problems

讲座摘要

We first develop random batch methods for classical  interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from O(N^2) per time step to O(N), for a system with N particles with binary interactions. For one of the methods, we give a particle number independent error estimate under some special interactions.  

For quantum N-body Schrodinger equation, we obtain, for pair-wise random interactions, a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is uniform in N > 1 and independent of the Planck constant \hbar. To this goal we need to introduce a new metric specially tailored to handle at the same time the difficulties pertaining to the small \hbar regime (classical limit), and those pertaining to the large N regime (mean-field limit).  

The classical part was a joint work with Lei Li and Jian-Guo Liu, while the quantum part was with Francois Golse and Thierry Paul.  


This is a joint Math Department-ICM Colloquium lecture.


个人简介

金石,现为上海交通大学自然科学研究院院长,数学学院讲席教授。先后获北京大学学士学位,美国亚利桑那大学博士学位,历任美国纽约大学库朗数学研究所博士后,美国佐治亚理工学院助理教授、副教授,美国威斯康星大学(麦迪逊)正教授,数学系系主任,Vilas 杰出成就教授,上海交通大学数学系讲席教授、系主任。

他同时担任上海应用数学中心联合主任,上海交通大学教育部科学工程计算重点实验室主任与人工智能数学基础中心主任。

他是冯康科学计算奖获得者(2001),美国数学会(AMS)首批会士(2012),工业与应用数学学会(SIAM)会士(2013),及2018年国际数学家大会邀请报告人。

他的研究方向包括动理学理论,量子动力学,不确定量化,粒子系统, 计算流体力学等。 他发表过170余篇学术论文,并获得过Springer 杂志Research in the Mathematical Sciences 创刊5年来四篇最佳论文奖之一(2019)。

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