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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2504.16701 |
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| _version_ | 1866910052114235392 |
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| author | Adler, V. E. Veselov, A. P. |
| author_facet | Adler, V. E. Veselov, A. P. |
| contents | We show that the equations of motion of the rigid body about centre of mass in the Newtonian field with a quadratic potential are special reductions of period-one closure of the Darboux dressing chain for the Schrödinger operators with matrix potentials. We show that the corresponding matrix Schrödinger operators are maximally finite-gap (in the sense that for all sufficiently large energies all solutions of the corresponding Schrödinger equation are bounded) and describe their spectrum explicitly. The general $2\times 2$-matrix case of the dressing chain, providing also some exotic matrix versions of the harmonic oscillator, is discussed in more detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spinning top in quadratic potential and matrix dressing chain Adler, V. E. Veselov, A. P. Mathematical Physics Spectral Theory 37J35, 70H06, 81R12 We show that the equations of motion of the rigid body about centre of mass in the Newtonian field with a quadratic potential are special reductions of period-one closure of the Darboux dressing chain for the Schrödinger operators with matrix potentials. We show that the corresponding matrix Schrödinger operators are maximally finite-gap (in the sense that for all sufficiently large energies all solutions of the corresponding Schrödinger equation are bounded) and describe their spectrum explicitly. The general $2\times 2$-matrix case of the dressing chain, providing also some exotic matrix versions of the harmonic oscillator, is discussed in more detail. |
| title | Spinning top in quadratic potential and matrix dressing chain |
| topic | Mathematical Physics Spectral Theory 37J35, 70H06, 81R12 |
| url | https://arxiv.org/abs/2504.16701 |