@article {26574,
	title = {An advective-spectral-mixed method for time-dependent many-body Wigner simulations},
	journal = {SIAM Journal on Scientific Computing},
	volume = {38},
	year = {2016},
	pages = {B491{\textendash}B520},
	abstract = {As a phase space language for quantum mechanics,\&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.\&nbsp;However, deterministic numerical solutions have been almost exclusively confined to one-dimensional one-body systems\&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.\&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,\&nbsp;for the system consisting of identical particles, \&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,\&nbsp;where the third-order accuracy against both grid spacing and time stepping is observed. \&nbsp;},
	url = {http://www.siam.org/journals/sisc/38-4/M105137.html},
	author = {Yunfeng Xiong and Zhenzhu Chen and Sihong Shao}
}
