Universal Second-Order Phase Transition from Integrability to Chaos
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915808748240896 |
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| 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 report a dynamical phase transition from integrability to non-integrability in a simple oval-like billiard with boundary $R(θ)=1+ε\cos(pθ)$. For $ε=0$, the phase space is {\it foliated} by invariant curves corresponding to periodic or quasiperiodic motion, whereas for small $ε$ a thin chaotic layer separates rotational and librational trajectories. As $ε$ increases, this layer grows according to a well-defined scaling law whose chaotic dispersion follows $ω_{\rm rms,sat}\simε^{\tildeα}$, where the exponent $\tildeα$ coincides with those of the Fermi-Ulam model, periodically corrugated waveguides, and a family of discrete mappings, revealing a universal mechanism for the onset of chaos in weakly perturbed integrable systems. The deviation of the reflection angle in the billiard, $ω_{\rm rms,sat}$, acts as an order parameter: it vanishes continuously as $ε\to 0$, signalling an ordered (integrable) phase, while its susceptibility $χ=dω_{\rm rms,sat}/dε$ diverges, indicating a second-order phase transition. A symmetry breaking and an analytically solvable diffusion process complete the near-critical phenomenology. These results establish a unified framework for the emergence of chaos from integrability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17802 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Second-Order Phase Transition from Integrability to Chaos Leonel, Edson D. de Almeida, Mayla A. M. Tarigo, Juan Pedro Marti, Arturo C. Oliveira, Diego F. M. Chaotic Dynamics We report a dynamical phase transition from integrability to non-integrability in a simple oval-like billiard with boundary $R(θ)=1+ε\cos(pθ)$. For $ε=0$, the phase space is {\it foliated} by invariant curves corresponding to periodic or quasiperiodic motion, whereas for small $ε$ a thin chaotic layer separates rotational and librational trajectories. As $ε$ increases, this layer grows according to a well-defined scaling law whose chaotic dispersion follows $ω_{\rm rms,sat}\simε^{\tildeα}$, where the exponent $\tildeα$ coincides with those of the Fermi-Ulam model, periodically corrugated waveguides, and a family of discrete mappings, revealing a universal mechanism for the onset of chaos in weakly perturbed integrable systems. The deviation of the reflection angle in the billiard, $ω_{\rm rms,sat}$, acts as an order parameter: it vanishes continuously as $ε\to 0$, signalling an ordered (integrable) phase, while its susceptibility $χ=dω_{\rm rms,sat}/dε$ diverges, indicating a second-order phase transition. A symmetry breaking and an analytically solvable diffusion process complete the near-critical phenomenology. These results establish a unified framework for the emergence of chaos from integrability. |
| title | Universal Second-Order Phase Transition from Integrability to Chaos |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2602.17802 |