题目：Negative particle method for the many-body quantum kinetic equation
报告人：Yunfeng Xiong（Beijing Normal University）
时间：2024年5月18日（星期六），10:00-11:00
地点：明德楼B201-1报告厅
摘要：The physical interest in quantum kinetic theory has increased the advances in the study of cold Bose gases in Bose{Einstein condensation and cold Fermi gases, as well as modelling degenerate plasmas during compression of the cold fuel and capsule shell in inertial confinement fusion. However, it is notoriously difficult to solve the quantum kinetic equation numerically due to the well-known curse of dimensionality. In this talk, we would like to discuss a class of negative particle method for solving many-body quantum kinetic equation, based on its branching random walk interpretation associated with negative weights. To alleviate the numerical sign problem inherited in the negative particle method, we suggest two approaches: The first is a variance reduction technique based on the stationary phase approximation to kill the redundant stochastic particles. The second is an adaptive particle annihilation algorithm, termed Sequential-clustering Particle Annihilation via Discrepancy Estimation (SPADE). Specifically, SPADE follows a divideand-conquer strategy: Adaptive clustering of particles via controlling their number-theoretic discrepancies and independent random matching in each cluster. Combining them together, we attempt to simulate the proton-electron couplings in 6-D and 12-D phase space. This talk is based on a series of works joint with Prof. Sihong Shao at Peking University.
