Scaling of highly excited Schrödinger-Poisson eigenstates and universality of their rotation curves
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908424716943360 |
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| author | Marangon, Gaia Ponno, Antonio Zanelli, Lorenzo |
| author_facet | Marangon, Gaia Ponno, Antonio Zanelli, Lorenzo |
| contents | This work provides a comprehensive numerical characterization of the excited spherically symmetric stationary states of the Schrödinger-Poisson problem. Through numerical computation of highly excited eigenstates, novel heuristic laws are proposed, which describe how their fundamental features scale with the excitation index $n$. Key characteristics of the eigenfunctions include: the effective support, which exhibits a parabolic dependence on the excitation index; the distances between adjacent nodes, whose pattern varies regularly with $n$; and the oscillation amplitude, which follows a power law with an exponent approaching $-1$ for large $n$. Based on the eigenfunctions, eigenvelocities are conveniently defined. They exhibit a mid-range oscillatory region with an average linear trend, whose slope approaches zero in the large $n$ limit; and they are characterized by heuristic scaling relationships with the excitation index $n$, revealing an intrinsic universal behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling of highly excited Schrödinger-Poisson eigenstates and universality of their rotation curves Marangon, Gaia Ponno, Antonio Zanelli, Lorenzo Mathematical Physics This work provides a comprehensive numerical characterization of the excited spherically symmetric stationary states of the Schrödinger-Poisson problem. Through numerical computation of highly excited eigenstates, novel heuristic laws are proposed, which describe how their fundamental features scale with the excitation index $n$. Key characteristics of the eigenfunctions include: the effective support, which exhibits a parabolic dependence on the excitation index; the distances between adjacent nodes, whose pattern varies regularly with $n$; and the oscillation amplitude, which follows a power law with an exponent approaching $-1$ for large $n$. Based on the eigenfunctions, eigenvelocities are conveniently defined. They exhibit a mid-range oscillatory region with an average linear trend, whose slope approaches zero in the large $n$ limit; and they are characterized by heuristic scaling relationships with the excitation index $n$, revealing an intrinsic universal behavior. |
| title | Scaling of highly excited Schrödinger-Poisson eigenstates and universality of their rotation curves |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2502.05030 |