Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909450536747008 |
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| author | Klausen, Kristjan O. Ingvarsson, Snorri |
| author_facet | Klausen, Kristjan O. Ingvarsson, Snorri |
| contents | The Landau-Lifshitz-Gilbert equation for magnetization dynamics is recast into spinor form using the real-valued Clifford algebra (geometric algebra) of three-space. We show how the undamped case can be explicitly solved to obtain component-wise solutions, with clear geometrical meaning. Generalizations of the approach to include damping are formulated. The implications of the axial property of the magnetization vector are briefly discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra Klausen, Kristjan O. Ingvarsson, Snorri Classical Physics Mesoscale and Nanoscale Physics The Landau-Lifshitz-Gilbert equation for magnetization dynamics is recast into spinor form using the real-valued Clifford algebra (geometric algebra) of three-space. We show how the undamped case can be explicitly solved to obtain component-wise solutions, with clear geometrical meaning. Generalizations of the approach to include damping are formulated. The implications of the axial property of the magnetization vector are briefly discussed. |
| title | Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra |
| topic | Classical Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2501.03798 |