Year: 2019
Communications in Computational Physics, Vol. 25 (2019), Iss. 3 : pp. 871–910
Abstract
To implement the Wigner branching random walk, the particle carrying a signed weight, either −1 or +1, is more friendly to data storage and arithmetic manipulations than that taking a real-valued weight continuously from −1 to +1. The former is called a signed particle and the latter a weighted particle. In this paper, we propose two efficient strategies to realize the signed-particle implementation. One is to interpret the multiplicative functional as the probability to generate pairs of particles instead of the incremental weight, and the other is to utilize a bootstrap filter to adjust the skewness of particle weights. Performance evaluations on the Gaussian barrier scattering (2D) and a Helium-like system (4D) demonstrate the feasibility of both strategies and the variance reduction property of the second approach. We provide an improvement of the first signed-particle implementation that partially alleviates the restriction on the time step and perform a thorough theoretical and numerical comparison among all the existing signed-particle implementations. Details on implementing the importance sampling according to the quasi-probability density and an efficient resampling or particle reduction are also provided.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0141
Communications in Computational Physics, Vol. 25 (2019), Iss. 3 : pp. 871–910
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: Wigner equation branching random walk signed particle bootstrapping weighted particle Monte Carlo method quantum dynamics importance sampling resampling particle reduction.