Diffusion in symplectic maps.
Diffusion in symplectic maps.
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辛图中的扩散。
DOI：
10.1103/physreva.41.4143
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
J. Meiss
中科院分区：
文献类型：
--
作者：
H. Kook;J. Meiss
采用特征函数法求得辛图的扩散张量。在最低阶上获得拟线性结果，并开发出一系列高阶相关性。使用 Froeschl'e 的四维示例给出了理论与数值实验的比较。对于中等大的参数，实验与理论非常吻合。讨论了“厚层”情况下的 Arnol'd 扩散。结果表明，即使在零耦合的极限下，一个规范平面中的短时相关性也会影响另一平面中的扩散。 Froeschl'e 示例中存在加速器模式，并会导致扩散发散，但这些仅在加速区域包含在系综中时才会出现。
The characteristic function method is used to obtain the diffusion tensor for symplectic maps. At lowest order the quasilinear result is obtained, and a series in higher-order correlations is developed. Comparison of the theory to numerical experiments is given using a four-dimensional example of Froeschl\'e. The experiments agree well with the theory for moderately large parameters. Arnol'd diffusion for the ``thick-layer'' case is discussed. It is shown that the short-time correlations in one canonical plane affect the diffusion in the other plane even in the limit of zero coupling. Accelerator modes exist for the Froeschl\'e example and cause divergences in the diffusion, but these only appear when the accelerating region is included in the ensemble.