<?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%">Sihong Shao</style></author><author><style face="normal" font="default" size="100%">Yunfeng Xiong</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A branching random walk method for many-body Wigner quantum dynamics</style></title><secondary-title><style face="normal" font="default" size="100%">Numerical Mathematics: Theory, Methods and Applications</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://doi.org/10.4208/nmtma.OA-2018-0074</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">21-71</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">A branching random walk algorithm for many-body Wigner&amp;nbsp;equations and its numerical applications for quantum dynamics in phase space&amp;nbsp;are proposed and analyzed in this paper.&amp;nbsp;Using an auxiliary function, the truncated Wigner&amp;nbsp;equation and its adjoint form are cast into integral formulations, which can be then reformulated into renewal-type equations with probabilistic interpretations.&amp;nbsp;We prove that the first moment of a branching random walk is the solution for the adjoint equation.&amp;nbsp;With the help of the additional degree of freedom offered by the auxiliary function,&amp;nbsp;we are able to produce a weighted-particle implementation of the branching random walk.&amp;nbsp;In contrast to existing signed-particle implementations,&amp;nbsp;this weighted-particle one shows a key capacity of variance reduction&amp;nbsp;by increasing the constant auxiliary function and has no time discretization errors.&amp;nbsp;Several canonical numerical experiments on the 2D Gaussian barrier scattering&amp;nbsp;and a 4D Helium-like system validate our theoretical findings, and demonstrate the accuracy, the efficiency,&amp;nbsp;and thus the computability of the proposed weighted-particle Wigner branching random walk algorithm.</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue></record></records></xml>