<?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%">Jean Michel Sellier</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">   Comparison of deterministic and stochastic methods for time-dependent Wigner simulations</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Computational Physics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1016/j.jcp.2015.08.002</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">300</style></volume><pages><style face="normal" font="default" size="100%">167-185</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed.&amp;nbsp;While it has been thoroughly validated against physical benchmarks,&amp;nbsp;no technical study about its numerical accuracy has been performed.&amp;nbsp;To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method.&amp;nbsp;An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions.&amp;nbsp;Several different numerical tests involving the time-dependent evolution of a quantum wave-packet are performed and discussed&amp;nbsp;in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy. &amp;nbsp;</style></abstract></record></records></xml>