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On Nonlinear Schrödinger Equation as a Model for Dark Matter

Comments on Galactic Collisions, Supermassive Black Holes and Analogue Laboratory Implementations
  • Angel Paredes
  • Humberto Michinel
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

In this chapter, we present an overview of the problem of dark matter and the scalar field dark matter model, which assumes the existence of a cosmological matter wave describing a condensate of ultralight axions. The mathematical description is in terms of a nonlinear Schrödinger-Poisson system of equations. We introduce the framework in a pedagogical way, for readers interested in nonlinear science assuming no prior knowledge of cosmology. We describe a split-step pseudospectral numerical method which is useful to compute the evolution in time of dark matter distributions. We then discuss two aspects of the model: an explanation of the so-called offsets between dark matter and stars in galactic clusters and the laws relating supermassive black holes and dark matter distributions. Finally, we emphasize the formal connections to particular situations of other physical systems, including cold atom Bose-Einstein condensates and laser beam propagation in thermo-optical media, which may lead to tabletop laboratory analogues of cosmological phenomena.

Keywords

Dark matter Axion-like particle Solitons Nonlinear Schrödinger equation Schrödinger-Poisson equation Nonlocal nonlinearities Scalar field dark matter 

Notes

Acknowledgements

We acknowledge financial support from Ministerio de Economía y Competitividad (MINECO) through grants FIS2014-58117-P, FIS2014-61984-EXP, and from Xunta de Galicia through grant GPC2015/019.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Área de óptica, Departamento de Física AplicadaOurenseSpain
  2. 2.Área de óptica, Escola de Enxeñaría AeroespacialOurenseSpain

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