The Wigner Branching Random Walk: Efficient Implementation and Performance Evaluation (Communications in Computational Physics, 2018)
To implement the Wigner branching random walk, the particle carrying asigned weight, either −1 or +1, is more friendly to data storage and arithmetic manipulationsthan that taking a real-valued weight continuously from −1 to +1. Theformer is called a signed particle and the latter a weighted particle. In this paper, wepropose two efficient strategies to realize the signed-particle implementation. One isto interpret the multiplicative functional as the probability to generate pairs of particlesinstead of the incremental weight, and the other is to utilize a bootstrap filter toadjust the skewness of particle weights. Performance evaluations on the Gaussian barrierscattering (2D) and a Helium-like system (4D) demonstrate the feasibility of bothstrategies and the variance reduction property of the second approach. We provide animprovement of the first signed-particle implementation that partially alleviates therestriction on the time step and perform a thorough theoretical and numerical comparisonamong all the existing signed-particle implementations. Details on implementingthe importance sampling according to the quasi-probability density and an efficientresampling or particle reduction are also provided.