Year: 2019
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 1 : pp. 21–71
Abstract
A branching random walk algorithm for many-body Wigner equations and its numerical applications for quantum dynamics in phase space are proposed and analyzed in this paper. Using an auxiliary function, the truncated Wigner equation and its adjoint form are cast into integral formulations, which can be then reformulated into renewal-type equations with probabilistic interpretations. We prove that the first moment of a branching random walk is the solution for the adjoint equation. With the help of the additional degree of freedom offered by the auxiliary function, we are able to produce a weighted-particle implementation of the branching random walk. In contrast to existing signed-particle implementations, this weighted-particle one shows a key capacity of variance reduction by increasing the constant auxiliary function and has no time discretization errors. Several canonical numerical experiments on the 2D Gaussian barrier scattering and a 4D Helium-like system validate our theoretical findings, and demonstrate the accuracy, the efficiency, and thus the computability of the proposed weighted-particle Wigner branching random walk algorithm.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2018-0074
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 1 : pp. 21–71
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 51
-
Overcoming the Numerical Sign Problem in the Wigner Dynamics via Adaptive Particle Annihilation
Xiong, Yunfeng | Shao, SihongSIAM Journal on Scientific Computing, Vol. 46 (2024), Iss. 2 P.B107
https://doi.org/10.1137/22M1498279 [Citations: 0] -
A computational approach for investigating Coulomb interaction using Wigner–Poisson coupling
Benam, Majid | Ballicchia, Mauro | Weinbub, Josef | Selberherr, Siegfried | Nedjalkov, MihailJournal of Computational Electronics, Vol. 20 (2021), Iss. 2 P.775
https://doi.org/10.1007/s10825-020-01643-x [Citations: 7] -
Stochastic Approaches to Electron Transport in Micro- and Nanostructures
Transient Quantum Particle Attributes
Nedjalkov, Mihail | Dimov, Ivan | Selberherr, Siegfried2021
https://doi.org/10.1007/978-3-030-67917-0_15 [Citations: 0] -
Solving the Wigner equation with signed particle Monte Carlo for chemically relevant potentials
Wang, Yu | Simine, LenaThe Journal of Chemical Physics, Vol. 155 (2021), Iss. 3
https://doi.org/10.1063/5.0055603 [Citations: 2] -
A Characteristic-Spectral-Mixed Scheme for Six-Dimensional Wigner–Coulomb Dynamics
Xiong, Yunfeng | Zhang, Yong | Shao, SihongSIAM Journal on Scientific Computing, Vol. 45 (2023), Iss. 6 P.B906
https://doi.org/10.1137/22M1494294 [Citations: 2] -
Branching Random Walk Solutions to the Wigner Equation
Shao, Sihong | Xiong, YunfengSIAM Journal on Numerical Analysis, Vol. 58 (2020), Iss. 5 P.2589
https://doi.org/10.1137/19M1272408 [Citations: 2]