# A Branching Random Walk Method for Many-Body Wigner Quantum Dynamics

@article{Shao2019ABR, title={A Branching Random Walk Method for Many-Body Wigner Quantum Dynamics}, author={Sihong Shao and Yunfeng Xiong}, journal={Numerical Mathematics: Theory, Methods and Applications}, year={2019} }

A branching random walk algorithm for the many-body Wigner equation and its numerical applications for quantum dynamics in phase space are proposed and analyzed. After introducing an auxiliary function, the (truncated) Wigner equation is cast into the integral formulation as well as its adjoint correspondence, both of which can be reformulated into the renewal-type equations and have transparent probabilistic interpretation. We prove that the first moment of a branching random walk happens to…

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An improvement of the first signed-particle implementation that partially alleviates the restriction on the time step is provided and a thorough theoretical and numerical comparison among all the existing signed- particle implementations is performed.

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