<?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%">Zhenzhu Chen</style></author><author><style face="normal" font="default" size="100%">Sihong Shao</style></author><author><style face="normal" font="default" size="100%">Wei Cai</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences</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%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1016/j.jcp.2019.06.047</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">396</style></volume><pages><style face="normal" font="default" size="100%">54-71</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We propose a high order numerical method for computing time dependent 4-D Wigner equation with unbounded potential and study a canonical quantum double-slit interference problem. To address the difficulties of 4-D phase space computations and higher derivatives from the Moyal expansion of nonlocal pseudo-differential operator for unbounded potentials, an operator splitting technique is adopted to decompose the 4-D Wigner equation into two sub-equations, which can be computed analytically or numerically with high efficiency. The first sub-equation contains only linear convection term in $(\bm x, t)$-space and can be solved with an advective method, while the second involves the pseudo-differential term and can be approximated by a plane wave expansion in $\bm k$-space. By exploiting properties of Fourier transformation,&amp;nbsp; the expansion coefficients for the second sub-equation have explicit forms and the resulting scheme is shown to be unconditionally stable for any higher derivatives of the Moyal expansion, ensuring the feasibility of the 4-D Wigner numerical simulations for quantum double-slit interferences. Numerical experiments demonstrate the spectral convergence in $(\bm x, \bm k)$-space and provide highly accurate information on the number, position, and intensity of the interference fringes for different types of slits, quantum particle masses, and initial states (pure and mixed).</style></abstract></record></records></xml>