@article {26628,
	title = {   The Wigner branching random walk: Efficient implementation and performance evaluation},
	journal = {Communications in Computational Physics},
	volume = {25},
	year = {2019},
	pages = {871-910},
	abstract = {To implement the Wigner branching random walk, the particle carrying a signed weight, either $-1$ or $+1$, is more friendly to data storage and arithmetic manipulations than that taking a real-valued weight continuously from $-1$ to $+1$. The former is called a signed particle and the latter a weighted particle. In this paper, we propose two efficient strategies to realize the signed-particle implementation. One is to interpret the multiplicative functional as the probability to generate pairs of particles instead of the incremental weight, and the other is to utilize a bootstrap filter to adjust the skewness of particle weights. Performance evaluations on the Gaussian barrier scattering (2D) and a Helium-like system (4D) demonstrate the feasibility of both strategies and the variance reduction property of the second approach. We provide an improvement of the first signed-particle implementation that\&nbsp;partially alleviates the restriction on the time step and perform a thorough theoretical and numerical comparison among all the existing signed-particle implementations. Details on implementing the importance sampling according to the quasi-probability density and an efficient resampling or particle reduction are also provided.},
	url = {https://www.global-sci.org/uploads/Issue/CiCP/v25n3/253_871.pdf},
	author = {Yunfeng Xiong and Sihong Shao}
}
