Integrator for general spin-s Gross-Pitaevskii systems

We provide an algorithm, i-SPin 2, for evolving general spin -s Gross-Pitaevskii or nonlinear Schrodinger 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 Schrodinger 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.

Automated summary

The algorithm i-SPin 2 is designed for evolving spin systems with various interactions. It considers different spin-multiplicity states and allows for spatially varying vector potentials that couple to the spin density. The algorithm has applications in laboratory systems, cosmology, and astrophysics.