论文标题
在开放式标准地图中的扩散和逃生时间
Diffusion and escape times in the open-leaky standard map
论文作者
论文摘要
我们研究了二维标准图中运输现象与逃生速率统计数据之间的联系。为了拥有开放的相空间，我们让动量坐标自由变化，并且仅限制角度与周期性边界条件。我们还沿着颗粒可能离开系统的动量轴对称地定义了一对人造孔。由于泄漏的结果，可以分析扩散，仅利用幸存的颗粒集合。我们介绍了扩散系数如何取决于逃生区域的大小和位置。由于加速器模式，因此扩散与系统的控制参数密切相关，因此我们还研究了扰动强度的影响。数值模拟表明，短时逃生统计量不会遵循众所周知的指数衰减，尤其是对于大量的扰动参数。逃生方向的分析还支持这张图片，因为大量粒子跳过了泄漏，并在长期游览相位偏远区域后离开系统。
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with periodic boundary condition. We also define a pair of artificial holes placed symmetrically along the momentum axis where the particles might leave the system. As a consequence of the leaks the diffusion can be analysed making use of only the ensemble of survived particles. We present how the diffusion coefficient depends on the size and position of the escape regions. Since the accelerator modes and, thus, the diffusion are strongly related to the system's control parameter, we also investigate effects of the perturbation strength. Numerical simulations show that the short-time escape statistics does not follow the well-known exponential decay especially for large values of perturbation parameters. The analysis of the escape direction also supports this picture as a significant amount of particles skip the leaks and leave the system just after a longtime excursion in the remote zones of the phase space.
