特殊扩散：区分正常和异常随机游动
Paradoxical diffusion: Discriminating between normal and anomalous random walks
摘要：
通常，正常扩散行为的特征在于第二中心矩对时间的线性依赖性，$< x^2(t) >\propto t$，而异常行为预计将显示不同的时间依赖性，$ < x^2(t) > \propto t^δ$，其中$δ<1$用于亚扩散运动，$δ>1$用于超扩散运动。在这里，我们表明，这种资格，如果直接应用，可能会产生误导：有异常的运输运动揭示完美的“正常”扩散字符（$< x^2(t) >\propto t$），但在性质上是非马尔可夫和非高斯。我们使用最近开发的框架\cite [Phys. Rev. E \textbf{75}，056702（2007）]{magdziarz 2007 b}的蒙特卡罗模拟，它结合了异常扩散统计的时间和空间，并创建这样一个扩展的随机游走的轨迹。对于特殊选择的稳定性指标描述统计的等待时间和跳跃长度，反常扩散的系综分析显示隐藏的时间记忆效应，可以正确地检测到只有通过检查的正式标准Markovianity（履行查普曼-Kolmogorov方程）。
英文摘要：
Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $< x^2(t) >\propto t$, while anomalous behavior is expected to show a different time dependence, $ < x^2(t) > \propto t^δ$ with $δ<1$ for subdiffusive and $δ>1$ for superdiffusive motions. Here we demonstrate that this kind of qualification, if applied straightforwardly, may be misleading: There are anomalous transport motions revealing perfectly "normal" diffusive character ($< x^2(t) >\propto t$), yet being non-Markov and non-Gaussian in nature. We use recently developed framework \cite[Phys. Rev. E \textbf{75}, 056702 (2007)]{magdziarz2007b} of Monte Carlo simulations which incorporates anomalous diffusion statistics in time and space and creates trajectories of such an extended random walk. For special choice of stability indices describing statistics of waiting times and jump lengths, the ensemble analysis of paradoxical diffusion is shown to hide temporal memory effects which can be properly detected only by examination of formal criteria of Markovianity (fulfillment of the Chapman-Kolmogorov equation).
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