Role of infinite invariant measure in deterministic subdiffusion.
Role of infinite invariant measure in deterministic subdiffusion.
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DOI：
10.1103/physreve.82.030102
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
Takuma Akimoto;T. Miyaguchi
中科院分区：
文献类型：
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作者：
Takuma Akimoto;T. Miyaguchi
从无限遍历理论的观点出发，研究了确定性次扩散输运系数的统计性质。我们发现，平均扩散系数是由约化映射的无穷不变测度来刻画的。我们还发现，当时间差远远小于总观测时间时，时均均方位移与时间差成线性关系。此外，扩散系数成为一个随机变量，其极限分布符合被称为Mittag-Leffler分布的普遍定律。
Statistical properties of the transport coefficient for deterministic subdiffusion are investigated from the viewpoint of infinite ergodic theory. We find that the averaged diffusion coefficient is characterized by the infinite invariant measure of the reduced map. We also show that when the time difference is much smaller than the total observation time, the time-averaged mean square displacement depends linearly on the time difference. Furthermore, the diffusion coefficient becomes a random variable and its limit distribution is characterized by the universal law called the Mittag-Leffler distribution.