Describing a Universal Critical Behavior in a transition from order to chaos
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917283771711488 |
|---|---|
| author | Leonel, Edson D. de Almeida, Mayla A. M. Tarigo, Juan Pedro Marti, Arturo C. Oliveira, Diego F. M. |
| author_facet | Leonel, Edson D. de Almeida, Mayla A. M. Tarigo, Juan Pedro Marti, Arturo C. Oliveira, Diego F. M. |
| contents | We present a comprehensive discussion of a transition from integrability to non-integrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter $ε$, which modifies the boundary shape from circular, corresponding to $ε=0$ and an integrable dynamics, to oval for $ε\neq 0$, where non-integrability emerges. The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, we characterise the diffusive spreading of ensembles of trajectories and identify an observable, $ω_{rms,{\rm sat}}$, which plays the role of an order parameter for the transition. For small deformations, the saturation value of the diffusion obeys the scaling law $ω_{rms,{\rm sat}}\proptoε^{\tildeα}$, with a critical exponent $\tildeα=0.507(2)$, vanishing continuously as $ε\rightarrow 0$. The associated susceptibility, $χ=dω_{rms,{\rm sat}}/dε$, diverges in the same limit, signalling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17810 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Describing a Universal Critical Behavior in a transition from order to chaos Leonel, Edson D. de Almeida, Mayla A. M. Tarigo, Juan Pedro Marti, Arturo C. Oliveira, Diego F. M. Chaotic Dynamics We present a comprehensive discussion of a transition from integrability to non-integrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter $ε$, which modifies the boundary shape from circular, corresponding to $ε=0$ and an integrable dynamics, to oval for $ε\neq 0$, where non-integrability emerges. The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, we characterise the diffusive spreading of ensembles of trajectories and identify an observable, $ω_{rms,{\rm sat}}$, which plays the role of an order parameter for the transition. For small deformations, the saturation value of the diffusion obeys the scaling law $ω_{rms,{\rm sat}}\proptoε^{\tildeα}$, with a critical exponent $\tildeα=0.507(2)$, vanishing continuously as $ε\rightarrow 0$. The associated susceptibility, $χ=dω_{rms,{\rm sat}}/dε$, diverges in the same limit, signalling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics. |
| title | Describing a Universal Critical Behavior in a transition from order to chaos |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2602.17810 |