发表机构
School of Electrical Engineering and Computer Science, University of North Dakota; Departamento de Física, Unesp - Universidade Estadual Paulista（北达科他大学电气与计算机工程学院; 圣保罗州立大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过随机游走和台球系统揭示从可积性到混沌的一阶不连续相变，其特征为序参量跳跃、临界慢化及普适指数(0,1/2,-2)，证明了一类共同的动力学相变机制。
AI 中文摘要
我们利用受限随机游走和确定性台球型弹球系统研究从可积性到混沌的不连续路径。在这两个系统中，平稳扩散可观测量在相变点表现出有限跳跃：它在未扰动极限下消失，但对于任意小的非零扰动趋近于一个有限的、由几何控制的值，提供了一阶相变的特征序参量标志。尽管存在这种不连续性，弛豫时间尺度在接近相变时发散，揭示了临界慢化现象。两个模型都表现出正常扩散，β=1/2，一个与扰动无关的平稳态，α=0，以及交叉迭代尺度n_x∝λ^{-2}，得到z=-2，其中λ表示相应的扰动参数。共同的指数集(α,β,z)=(0,1/2,-2)源于相同的粗粒化机制：在有限可达域内的正常扩散，其扩散系数在相变点二次方地消失。随机输运与确定性混沌散射之间的一致性为不连续动力学相变的共同类别提供了有力证据，并将相变的统计力学描述扩展到可积性破缺动力学。
英文摘要
We investigate a discontinuous route from integrability to chaos using a confined stochastic random walk and a deterministic stadium-like billiard. In both systems, the stationary diffusive observable exhibits a finite jump at the transition: it vanishes at the unperturbed limit but approaches a finite, geometry-controlled value for arbitrarily small nonzero perturbations, providing the characteristic order-parameter signature of a first-order transition. Despite this discontinuity, the relaxation timescale diverges as the transition is approached, revealing critical slowing down. Both models exhibit normal diffusion with $β=1/2$, a perturbation-independent stationary state with $α=0$, and a crossover iteration scaling as $n_x\proptoλ^{-2}$, yielding $z=-2$, where $λ$ denotes the corresponding perturbation parameter. The common exponent set $(α,β,z)=(0,1/2,-2)$ originates from the same coarse-grained mechanism: normal diffusion within a finite accessible domain with a diffusion coefficient that vanishes quadratically at the transition. The agreement between stochastic transport and deterministic chaotic scattering provides strong evidence for a common class of discontinuous dynamical transitions and extends the statistical-mechanics description of phase transitions to integrability-breaking dynamics.
