@article {26625,
	title = {   Comparison of deterministic and stochastic methods for time-dependent Wigner simulations},
	journal = {Journal of Computational Physics},
	volume = {300},
	year = {2015},
	pages = {167-185},
	abstract = {Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed.\&nbsp;While it has been thoroughly validated against physical benchmarks,\&nbsp;no technical study about its numerical accuracy has been performed.\&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.\&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.\&nbsp;Several different numerical tests involving the time-dependent evolution of a quantum wave-packet are performed and discussed\&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. \&nbsp;},
	url = {http://dx.doi.org/10.1016/j.jcp.2015.08.002},
	author = {Sihong Shao and Jean Michel Sellier}
}
