Distribution of regularized three-body phase-volume
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912312590336000 |
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| author | Dandekar, Yogesh Kol, Barak |
| author_facet | Dandekar, Yogesh Kol, Barak |
| contents | The micro-canonical phase-space volume for the three-body problem is a topic of intrinsic interest. Within the flux-based statistical theory, it provides a means to predict the scale of disintegration times for non-hierarchical systems. While the bare phase-volume diverges, arXiv:2205.04294 (Paper I) showed that a regularized version can be defined. Building on Paper I, which determined the regularized phase-volume for a given energy $\barσ(E)$, this paper extends the analysis to its distribution over angular momentum, $\barσ(E,L)$. Through analytical integrations, we reduce the problem to a 3d numerical integration, a step up in complexity from the 2d integration required for $\barσ(E)$. We provide regularized phase-volume values for several mass sets across a range of $E$ and $L$, validated through an $L$-integration test. Notably, the values remain positive for all tested parameters, lending further support to the validity of the chosen regularization procedure. For high values of $L$ at fixed masses and $E$, we observe a strong suppression of $\barσ(E,L)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distribution of regularized three-body phase-volume Dandekar, Yogesh Kol, Barak Earth and Planetary Astrophysics Statistical Mechanics High Energy Physics - Theory Classical Physics The micro-canonical phase-space volume for the three-body problem is a topic of intrinsic interest. Within the flux-based statistical theory, it provides a means to predict the scale of disintegration times for non-hierarchical systems. While the bare phase-volume diverges, arXiv:2205.04294 (Paper I) showed that a regularized version can be defined. Building on Paper I, which determined the regularized phase-volume for a given energy $\barσ(E)$, this paper extends the analysis to its distribution over angular momentum, $\barσ(E,L)$. Through analytical integrations, we reduce the problem to a 3d numerical integration, a step up in complexity from the 2d integration required for $\barσ(E)$. We provide regularized phase-volume values for several mass sets across a range of $E$ and $L$, validated through an $L$-integration test. Notably, the values remain positive for all tested parameters, lending further support to the validity of the chosen regularization procedure. For high values of $L$ at fixed masses and $E$, we observe a strong suppression of $\barσ(E,L)$. |
| title | Distribution of regularized three-body phase-volume |
| topic | Earth and Planetary Astrophysics Statistical Mechanics High Energy Physics - Theory Classical Physics |
| url | https://arxiv.org/abs/2501.02013 |