<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Yunfeng Xiong</style></author><author><style face="normal" font="default" size="100%">Sihong Shao</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">   The Wigner branching random walk: Efficient implementation and performance evaluation</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Computational Physics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.global-sci.org/uploads/Issue/CiCP/v25n3/253_871.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">871-910</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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&amp;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.</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue></record></records></xml>