i-SPin: An integrator for multicomponent Schrödinger-Poisson systems with self-interactions by Mudit Jain et al. on Tuesday 22 November

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.

arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.08433v2