Overcoming the numerical sign problem in Wigner dynamics via particle annihilation
报告题目(Title)：Overcoming the numerical sign problem in Wigner dynamics via particle annihilation
报告人(Speaker)：熊云丰（北京大学）
地点(Place)： 教二105
时间(Time)：2021年9月27日13:30-14:30
邀请人(Inviter)：陈华杰
报告摘要
The infamous numerical sign problem poses a fundamental obstacle to the branching random walk algorithm for the Wigner quantum dy-namics. Although the existing particle annihilation via uniform mesh significantly alleviates the sign problem when dimensionality D<=4, the setting of regular grids gives rise to a formidable challenge in both its efficiency and data storage when D>=6 due to the curse of dimen-sionality. We propose an adaptive particle annihilation, termed se-quential-clustering particle annihilation via discrepancy estimation (SPADE), to overcome the numerical sign problem. SPADE consists of adaptive clustering of particles via controlling their number-theoretic discrepancies and independent random matching in each group, and may learn the minimal amount of particles that can accurately capture the oscillating nature of the Wigner function. Combining SPADE with a recently proposed variance reduction technique via the stationary phase approximation, we attempt to simulate the Wigner dynamics in 6-D phase space. Its numerical accuracy is verified by a thorough comparison between the results produced by our recently developed 6-D deterministic Wigner solver.
