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arXiv · 2305.01675

i-SPin 2: An integrator for general spin-s Gross-Pitaevskii systems

Mudit Jain·Mustafa A. Amin·Han Pu
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Abstract

We provide an algorithm for evolving general spin-$s$ Gross-Pitaevskii / non-linear Schr\"odinger 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 Schr\"odinger 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/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.

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Mudit Jain, Mustafa A. Amin, Han Pu. 2023-05-02. i-SPin 2: An integrator for general spin-s Gross-Pitaevskii systems. https://doi.org/10.1103/physreve.108.055305

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