i-SPin 2: An integrator for general spin-s Gross-Pitaevskii systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909143964581888 |
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| author | Jain, Mudit Amin, Mustafa A. Pu, Han |
| author_facet | Jain, Mudit Amin, Mustafa A. Pu, Han |
| contents | We provide an algorithm for evolving general spin-$s$ Gross-Pitaevskii / non-linear 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/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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01675 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | i-SPin 2: An integrator for general spin-s Gross-Pitaevskii systems Jain, Mudit Amin, Mustafa A. Pu, Han Quantum Gases Cosmology and Nongalactic Astrophysics Pattern Formation and Solitons We provide an algorithm for evolving general spin-$s$ Gross-Pitaevskii / non-linear 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/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. |
| title | i-SPin 2: An integrator for general spin-s Gross-Pitaevskii systems |
| topic | Quantum Gases Cosmology and Nongalactic Astrophysics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2305.01675 |