i-SPin: an integrator for multicomponent Schr?dinger-Poisson systems with self-interactions

We provide an algorithm and a publicly available code to numerically evolve multicomponent Schrodinger-Poisson (SP) systems with a SO(n) symmetry, including at-tractive 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 interactions) introduce complexities related to mass and spin conservation which are not present in purely gravitational systems. We address them with an analytical solution for the `kick' step in the algorithm, where we are able to decouple the multicomponent system completely. 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 an expanding universe relevant for cosmology, and the inclusion of external potentials relevant for laboratory settings.

Automated summary

We have developed an algorithm and provided publicly available code to numerically evolve multicomponent Schrodinger-Poisson (SP) systems with a SO(n) symmetry, allowing for attractive or repulsive self-interactions in addition to gravity. The algorithm addresses complexities introduced by non-gravitational self-interactions, such as mass and spin conservation, through an analytical solution for the 'kick' step, which completely decouples the multicomponent system. The algorithm accurately preserves spin and mass, is reversible, and can be applied in cosmological and laboratory settings.