http://arxiv.org/abs/2211.08433
We provide an algorithm and a publicly available code to numerically evolve multicomponent Schr\”{o}dinger-Poisson (SP) systems, including attractive or repulsive self-interactions in addition to gravity. Focusing on the case where the SP system represents the non-relativistic limit of a massive vector field, non-gravitational self-interactions (in particular, spin-spin type interactions) introduce new challenges related to mass and spin conservation which are not present in purely gravitational systems. We address these challenges with an analytical solution for the non-trivial `kick’ step in the algorithm. Equipped with this analytical solution, the full field evolution is second order accurate, preserves spin and mass to machine precision, and is reversible. Our algorithm allows for: general $n$-component fields with SO$(n)$ symmetry, an expanding universe relevant for cosmology, and the inclusion of external potentials relevant for laboratory settings.
M. Jain and M. Amin
Thu, 17 Nov 22
34/63
Comments: 18 pages, 3 figures, 4 appendices. A python code based on our algorithm in provided at, this https URL . Animations of the numerical simulation results can be found at, this https URL