论文标题
标准地图中的不良行为
Sub-diffusive behavior in the Standard Map
论文作者
论文摘要
在这项工作中，我们研究了Chirikov-Taylor标准地图中的副延误行为。我们表明，在地图设置的混合相空间中存在的粘性现象可以被描述为连续的随机步行模型，并连接到异常扩散的理论背景。此外，我们选择了ULAM方法的变体来在数值上近似地图的perron-frobenius操作员，从而使我们能够通过特征值问题来计算异常扩散指数，与分数扩散方程相比。这里的结果证实了哈密顿图中异常运输文献中的其他发现，并且可以适合描述其他动态系统的运输特性。
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.
