报告人：Yunfeng Xiong (Peking University)
时间：2019-12-20 12:00-13:30
地点：Room 1560, Sciences Building No. 1
各位数院研究生同学：
研究生学术午餐会是在学院领导的大力支持下，由研究生会负责组织的系列学术交流活动。午餐会每次邀请一位同学作为主讲人，面向全院各专业背景的研究生介绍自己科研方向的基本问题、概念和方法，并汇报近期的研究成果和进展，是研究生展示自我、促进交流的学术平台。
研究生会已经举办了四十一期活动，我们将于2019年12月20日周五举办第四十二期学术午餐会活动，欢迎感兴趣的老师和同学积极报名参加。
报告人简介：熊云丰，2016年进入北京大学攻读计算数学博士学位，导师为邵嗣烘副教授。他的研究方向为计算量子力学、图谱理论及算法。他于2016年起入选“北京大学计算与应用数学拔尖博士生计划”，并荣获过校长奖学金和国家奖学金。他的研究课题是多体Wigner方程的随机算法，目前主要研究兴趣为多体量子问题的随机算法，以及概率论、调和分析和组合技术在蒙特卡洛方法中的综合应用。
Abstracct: The Monte Carlo integration of multi-dimensional oscillatory and determinantal functions is the fundamental problem in computational quantum mechanics, especially for simulating the many-body quantum system. Unfortunately, the efficiency of sampling is usually hampered by the infamous numerical sign problem due to the near-cancelation of contributions from positive and negative weights, or that from even or odd permutations, resulting in a very large variance in contrast to a small mean value. In this talk, we discuss several strategies to alleviate the numerical sign problem in simulating the quantum dynamics through the Wigner equation. We first discuss the weighted-particle branching random walk algorithm for the Wigner equation and shows that the setting of branching mechanism helps reduce the variance. However, the increase of computational cost in weighted-particle implementation sometimes offsets its advantage in variance reduction. Motivated from the fact the variance grows because the decay property of oscillatory integrals is ignored, our second contribution is to capture the decay property of oscillatory integrals by replacing the high-frequency components of the pseudo-differential operator with the principal term of its asymptotic expansion, known as the stationary phase approximation (SPA) in harmonic analysis. Finally, to further suppress the sign problem for a long-time simulation, we propose several resampling strategies to control the exponential growth of the particle number, as well as the variances. Combining these ingredients gives rises to an efficient and reliable stochastic algorithm for simulating the Wigner quantum dynamics, and several typical numerical experiments are presented to verify our theoretical findings as well as the accuracy.
报名方式：请有意参加的同学于2019年12月18日（周三）中午12点前填写报名问卷，复制问卷链接https://www.wjx.top/jq/52235700.aspx至浏览器或点击阅读原文进入问卷报名。
特别注意：如果您报名却没有参与活动，需要您自己承担已经购买的午餐费用。由于客观条件限制，本次午餐会的名额为25人，先报先得。
问卷如果填写成功即说明报名成功，请准时参加活动。如果临时有事不能参加请于12月19日中午12点前发邮件至smsxueshu@126.com。
如果问卷无法成功填写，说明报名人员已满，我们对难以成功报名的同学表示歉意。研究生会将继续探索午餐会的实现形式，争取更好地服务全体研究生同学。
