标题： 随机涨落导致粒子的禁止逃逸 显示英文标题

标题： Random fluctuation leads to forbidden escape of particles

摘要： 在哈密顿散射的背景下，描述了许多物理过程。以前的研究主要集中在从不变结构外部开始的轨迹上，因为从内部开始的轨迹预计会永远被困在那里。尽管这在确定性情况下是正确的，但我们表明，在有限小的随机波动场作用下，从Arnold-Kolmogorov-Moser（KAM）岛内部开始的轨迹会在有限时间内逃逸。由于随机扰动场的影响，非双曲动力学因此获得了双曲特征。结果是，从KAM曲线内部开始的轨迹以类似双曲的时间衰减分布逃逸，而留在散射区域的一组粒子的分形维数趋近于双曲系统的分形维数。我们展示了一个普遍的二次幂定律，将指数衰减与噪声的幅度联系起来。我们提出一个随机游走模型，将这种分布与噪声的幅度联系起来，并通过应用随机映射的数值研究来探讨这一现象。 显示英文摘要

摘要： A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser (KAM) islands escape within finite time. The non-hyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperbolic-like time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate this phenomena with a numerical study applying random maps.