标准映射中的次扩散行为
Sub-diffusive behavior in the Standard Map
摘要：
在这项工作中，我们调查的Chirikov-Taylor标准映射的亚扩散行为的存在。我们表明，粘性现象，目前在混合相空间的地图设置，可以表征为一个连续时间随机游走模型和连接到异常扩散的理论背景。此外，我们选择了一个变种的乌拉姆方法来数值近似的Perron-Frobenius算子的地图，使我们能够计算异常扩散指数通过本征值问题，相比分数扩散方程的解决方案。本文的结果证实了文献中关于哈密顿映射中反常输运的其他发现，并可适用于描述其他动力学系统的输运性质。
英文摘要：
In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time Random Walk model and connected to the theoretical background for anomalous diffusion. Additionally, we choose a variant of the Ulam method to numerically approximate the Perron-Frobenius operator for the map, allowing us to calculate the anomalous diffusion exponent via an eigenvalue problem, compared to the solution of the Fractional Diffusion Equation. The results here corroborate other findings in the literature of anomalous transport in Hamiltonian maps and can be suitable to describe transport properties of other dynamical systems.
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