Probability distribution in the Toda system: The singular route to a steady state
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912277240741888 |
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| author | Petrovic, Srdjan Starcevic, Nikola Stojanov, Nace Huang, Liang |
| author_facet | Petrovic, Srdjan Starcevic, Nikola Stojanov, Nace Huang, Liang |
| contents | This study reports on the evolution of the probability distribution in the configuration space of the two-dimensional Toda system. The distribution is characterized by singularities, which predominantly take two forms: double-cusped triangular lines and lines parallel to the equipotential line that defines the accessible region. Over time, the number of these singular patterns increases linearly. Consequently, at very large times, the singular patterns fully occupy the accessible area, resulting in a steady state probability distribution with a pronounced singular peak at the center. Changes in the singular patterns arise solely from the system's intrinsic dynamics rather than variations in its parameters, emphasizing the system's self-organizing nature over time. These results provide a deeper understanding of the collective motion of particles in symmetric, bounded, two-dimensional conservative systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probability distribution in the Toda system: The singular route to a steady state Petrovic, Srdjan Starcevic, Nikola Stojanov, Nace Huang, Liang Exactly Solvable and Integrable Systems This study reports on the evolution of the probability distribution in the configuration space of the two-dimensional Toda system. The distribution is characterized by singularities, which predominantly take two forms: double-cusped triangular lines and lines parallel to the equipotential line that defines the accessible region. Over time, the number of these singular patterns increases linearly. Consequently, at very large times, the singular patterns fully occupy the accessible area, resulting in a steady state probability distribution with a pronounced singular peak at the center. Changes in the singular patterns arise solely from the system's intrinsic dynamics rather than variations in its parameters, emphasizing the system's self-organizing nature over time. These results provide a deeper understanding of the collective motion of particles in symmetric, bounded, two-dimensional conservative systems. |
| title | Probability distribution in the Toda system: The singular route to a steady state |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.12415 |