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07-05-2023

Nonlocalization of singular potentials in quantum dynamics

Authors: Sihong Shao, Lili Su

Published in: Journal of Computational Electronics | Issue 4/2023

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Abstract

Nonlocal modeling has drawn more and more attention and becomes steadily more powerful in scientific computing. In this paper, we demonstrate the superiority of a first-principle nonlocal model—Wigner function—in treating singular potentials which are often used to model the interaction between point charges in quantum science. The nonlocal nature of the Wigner equation is fully exploited to convert the singular potential into the Wigner kernel with weak or even no singularity, and thus highly accurate numerical approximations are achievable, which are hardly designed when the singular potential is taken into account in the local Schrödinger equation. The Dirac delta function, the logarithmic, and the inverse power potentials are considered. Numerically converged Wigner functions under all these singular potentials are obtained with a fourth-order accurate operator splitting spectral method, and display many interesting quantum behaviors as well.

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Metadata
Title
Nonlocalization of singular potentials in quantum dynamics
Authors
Sihong Shao
Lili Su
Publication date
07-05-2023
Publisher
Springer US
Published in
Journal of Computational Electronics / Issue 4/2023
Print ISSN: 1569-8025
Electronic ISSN: 1572-8137
DOI
https://doi.org/10.1007/s10825-023-02042-8