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Comparison of two different integration methods for the (1+1)-dimensional Schrödinger-Poisson equation

We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schrödinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schrödinger equation with an auto-gravitating potential created by the wave function density...

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Bibliographic Details
Main Authors: Schwersenz, Nico (Author) , Loaiza, Victor (Author) , Zimmermann, Tim (Author) , Madroñero, Javier (Author) , Wimberger, Sandro (Author)
Format: Article (Journal)
Language:English
Published: 29 March 2024
In: Computer physics communications
Year: 2024, Volume: 300, Pages: 109192-1-109192-14
ISSN:1879-2944
DOI:10.1016/j.cpc.2024.109192
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.cpc.2024.109192
Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0010465524001152
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Author Notes:Nico Schwersenz, Victor Loaiza, Tim Zimmermann, Javier Madroñero, Sandro Wimberger
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Summary:We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schrödinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schrödinger equation with an auto-gravitating potential created by the wave function density itself. The latter is determined as a solution of Poisson's equation modelling, e.g., non-relativistic gravity. For reasons of complexity, we treat a one-dimensional version of the problem whose numerical integration is still challenging because of the extreme long-range forces (being constant in the asymptotic limit). Both of our methods, a Strang splitting scheme and a basis function approach using B-splines, are compared in numerical convergence and effectivity. Overall, our Strang-splitting evolution compares favourably with the B-spline method. In particular, by using an adaptive time-stepper rather large one-dimensional boxes can be treated. These results give hope for extensions to two spatial dimensions for not too small boxes and large evolution times necessary for describing, for instance, dark matter formation over cosmologically relevant scales.
Item Description:Gesehen am 11.11.2024
Physical Description:Online Resource
ISSN:1879-2944
DOI:10.1016/j.cpc.2024.109192

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