arXiv 2602.178102026-02-19nlin.CD

描述从有序到混沌的普遍临界行为的转变

Describing a Universal Critical Behavior in a transition from order to chaos

Unesp - 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

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AI总结：

该研究通过分析椭圆弹道中从可积到非可积的转变，发现临界行为与连续相变相似，揭示了混沌层的扩散特性及标度律。

摘要：

我们对一个具有静态边界的椭圆弹道中从可积到非可积的转变进行了全面讨论。这种转变由变形参数ε控制，它改变了边界的形状，从圆形（对应ε=0和可积动力学）到非零ε时的椭圆，其中非可积性出现。圆弹道的变形导致在相空间中形成一个混沌层，沿着一条明确的条带发展。通过引入一组变换来隔离这个混沌条带，我们表征了轨迹集合的扩散扩散并识别出一个可观测量ω_rms,sat，它在转变中扮演了顺序参数的角色。对于小变形，扩散饱和值遵循标度定律ω_rms,sat ∝ ε^~α，其中临界指数~α=0.507(2)，当ε→0时连续消失。相关的磁化率χ=dω_rms,sat/dε在相同极限下发散，表明存在类似于统计力学中二级（连续）相变中观察到的临界行为。

英文摘要：

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.

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