SEMINAR: Two different methods for solving the Schrödinger-Poisson Equation as a Model for Cold Dark Matter

Two different methods for solving the Schrödinger-Poisson Equation as a Model for Cold Dark Matter

Professor Sandro Wimberger

University of Parma, Italy

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We compare two different numerical methods to integrate in time spatially delocalized initial distributions of fuzzy dark matter. 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 non-relativistic gravity.  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 favorably with the B-spline method. By using an adaptive time-stepper large one-dimensional boxes can be treated. We understand and can control the unusual relaxation process occurring in one dimension due to the scale-free long-range interaction. These results give hope for extensions to two spatial dimensions for not too small boxes and large evolution times necessary for describing realistic dark matter formation over cosmologically relevant scales.

References

1. T. Zimmermann, N. Schwersenz, M. Pietroni, and S. Wimberger,

One-Dimensional Fuzzy Dark Matter Models: Structure Growth and Asymptotic Dynamics, Phys. Rev. D 103, 083018 (2021)

2. N. Schwersenz, V. Loaiza, T. Zimmermann, J. Madronero, and S. Wimberger,

Comparison of two different integration methods for the (1+1)-Dimensional Schroedinger-Poisson Equation, Comp. Phys. Comm. 300, 109192 (2024)

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Date: January 24^th, 2025

Time: 12pm-1pm NZST

Venue: SLT1 (303.G01, University of Auckland) and Zoom Meeting ID: 952 5705 8419

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