<?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%">Zhenzhu Chen</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%">An advective-spectral-mixed method for time-dependent many-body Wigner simulations</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM Journal on Scientific Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://epubs.siam.org/doi/10.1137/15M1051373</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">38</style></volume><pages><style face="normal" font="default" size="100%">B491–B520</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">As a phase space language for quantum mechanics,&amp;nbsp;the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems.&amp;nbsp;However, deterministic numerical solutions have been almost exclusively confined to one-dimensional one-body systems&amp;nbsp;and few results are reported even for one-dimensional two-body problems. This paper serves as the first attempt to solve the time-dependent many-body Wigner equation through a grid-based advective-spectral-mixed method. The main feature of the method is to resolve the linear advection in $(\bm{x},t)$-space by an explicit three-step characteristic scheme coupled with the piecewise cubic spline interpolation, while the Chebyshev spectral element method in $\bm k$-space is adopted for accurate calculation of the nonlocal pseudo-differential term.&amp;nbsp;Not only the time step of the resulting method is not restricted by the usual CFL condition and thus a large time step is allowed, but also the mass conservation can be maintained. In particular,&amp;nbsp;for the system consisting of identical particles, &amp;nbsp;the advective-spectral-mixed method can also rigorously preserve physical symmetry relations. The performance is validated through several typical numerical experiments, like the Gaussian barrier scattering, electron-electron interaction and a Helium-like system,&amp;nbsp;where the third-order accuracy against both grid spacing and time stepping is observed. &amp;nbsp;</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue></record></records></xml>