i-SPin: An integrator for multicomponent Schr\"{o}dinger-Poisson systems with self-interactions

TL;DR

This paper introduces i-SPin, a numerical algorithm and open-source code for evolving multicomponent Schrödinger-Poisson systems with self-interactions, applicable to cosmology and laboratory experiments, ensuring high accuracy and conservation.

Contribution

The paper presents a novel analytical solution for the 'kick' step in the algorithm, enabling decoupling of multicomponent systems with self-interactions, improving accuracy and conservation.

Findings

Algorithm achieves second-order accuracy.

Preserves spin and mass to machine precision.

Applicable to expanding universe and external potentials.

Abstract

We provide an algorithm and a publicly available code to numerically evolve multicomponent Schr\"{o}dinger-Poisson (SP) systems with a SO($n$) symmetry, 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 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.