arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2602.17802nlin.CD
收藏

从可积到混沌的普遍二级相变

Universal Second-Order Phase Transition from Integrability to Chaos

Universidade Estadual Paulista（圣保罗州立大学）；Universidad de la República（乌拉圭共和国大学）；University of North Dakota（北达科他大学）

Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo, Arturo C. Marti, Diego F. M. Oliveira

阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

研究揭示了从可积到混沌的普遍二级相变机制，通过分析弹奏板的相变行为，发现混沌出现的普遍规律。

摘要：

我们报告了一个简单的椭圆形弹奏板在边界R(θ)=1+εcos(pθ)下的动力学相变，从可积到非可积。对于ε=0，相空间被不变曲线所覆盖，对应于周期或拟周期运动；而对于小ε，薄混沌层将旋转轨迹和摆动轨迹分开。随着ε的增加，该层按照一个明确的标度定律增长，其混沌扩散遵循ω_rms,sat~ε^{~α}，其中指数~α与费米-乌拉模型、周期性波导和一组离散映射的指数相同，揭示了弱扰动可积系统中混沌出现的普遍机制。弹奏板中反射角的偏差ω_rms,sat作为序参量：当ε→0时，它连续消失，标志着有序（可积）相，而其susceptibilityχ=dω_rms,sat/dε发散，表明二级相变。对称性破坏和可解析求解的扩散过程完成了临界现象的近似描述。这些结果建立了一个统一的框架，用于从可积性中出现混沌。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑