Unified Geometric Perspective for Spin-1 Systems: Bridging Nematic Director and Majorana Stars
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918282984947712 |
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| author | Biguo, Jiangnan Ma, Rourou |
| author_facet | Biguo, Jiangnan Ma, Rourou |
| contents | We present a unified geometric approach for spin-1 systems that connects seemingly distinct geometric representations such as the nematic director, the Cartesian representation and the Majorana stellar representation. Starting from a product state of two distinguishable spin-1/2 particles, we provide a direct way to capture crucial geometric information. This perspective reveals the fundamental interplay between subspace projection and geometric constraints. This approach effectively maps magnetic solitons onto a kink model, allowing us to derive their equations of motion, a task not readily achieved with traditional methods. This simplified dynamical description reveals that the novel transition of these solitons in a harmonic trap corresponds to a fundamental transformation between kink and dip structures in the underlying geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06936 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unified Geometric Perspective for Spin-1 Systems: Bridging Nematic Director and Majorana Stars Biguo, Jiangnan Ma, Rourou Quantum Gases We present a unified geometric approach for spin-1 systems that connects seemingly distinct geometric representations such as the nematic director, the Cartesian representation and the Majorana stellar representation. Starting from a product state of two distinguishable spin-1/2 particles, we provide a direct way to capture crucial geometric information. This perspective reveals the fundamental interplay between subspace projection and geometric constraints. This approach effectively maps magnetic solitons onto a kink model, allowing us to derive their equations of motion, a task not readily achieved with traditional methods. This simplified dynamical description reveals that the novel transition of these solitons in a harmonic trap corresponds to a fundamental transformation between kink and dip structures in the underlying geometry. |
| title | Unified Geometric Perspective for Spin-1 Systems: Bridging Nematic Director and Majorana Stars |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2601.06936 |