The Wigner Branching Random Walk: Efficient Implementation and Performance Evaluation

The Wigner Branching Random Walk: Efficient Implementation and Performance Evaluation

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.