We provide an algorithm, i-SPin 2, for evolving general spin-$s$ Gross-Pitaevskii or nonlinear Schrödinger systems carrying a variety of interactions, where the $2s+1$ components of the “spinor” field represent the different spin-multiplicity states. We consider many nonrelativistic interactions up to quartic order in the Schrödinger field (both short and long range, and spin-dependent and spin-independent interactions), including explicit spin-orbit couplings. The algorithm allows for spatially varying external and/or self-generated vector potentials that couple to the spin density of the field. Our work can be used for scenarios ranging from laboratory systems such as spinor Bose-Einstein condensates (BECs), to cosmological or astrophysical systems such as self-interacting bosonic dark matter. As examples, we provide results for two different setups of spin-1 BECs that employ a varying magnetic field and spin-orbit coupling, respectively, and also collisions of spin-1 solitons in dark matter. Our symplectic algorithm is second-order accurate in time, and is extensible to the known higher-order-accurate methods.

• Received 13 June 2023
• Revised 23 August 2023
• Accepted 13 October 2023

DOI:https://doi.org/10.1103/PhysRevE.108.055305