Ultraslow diffusion in an exactly solvable non-Markovian random walk.
Ultraslow diffusion in an exactly solvable non-Markovian random walk.
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DOI：
10.1103/physreve.89.052110
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
M. D. da Silva;G. M. Viswanathan;J. Cressoni
中科院分区：
文献类型：
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作者：
M. D. da Silva;G. M. Viswanathan;J. Cressoni
研究了具有强记忆相关的一维离散非马尔可夫随机游动。不像Scher-Montroll连续时间随机游走，它可以通过定义一个等于随机游走步数的操作时间来使马尔可夫，我们研究的模型记录了整个行走的历史。这个新模型与Kumar，Harbola和Lindenberg最近提出的模型[Phys. Rev. E 82，021101（2010）]密切相关，不同之处在于，在我们的模型中，即使在子扩散的极端极限下，随机动力学也不会停止。令人惊讶的是，这种微小的差异导致了巨大的后果。我们在这里报告的主要结果是显示超低扩散和稳定扩散制度（即，本地化）。具体而言，运动方程的解析求解的前两个时刻，允许确定的赫斯特指数。几个异常扩散制度是明显的，从超扩散到亚扩散，以及超低和固定制度。我们提出了完整的相扩散图，沿着的持久性和感兴趣的区域中的统计研究。
We study a one-dimensional discrete-time non-Markovian random walk with strong memory correlations subjected to pauses. Unlike the Scher-Montroll continuous-time random walk, which can be made Markovian by defining an operational time equal to the random-walk step number, the model we study keeps a record of the entire history of the walk. This new model is closely related to the one proposed recently by Kumar, Harbola, and Lindenberg [Phys. Rev. E 82, 021101 (2010)], with the difference that in our model the stochastic dynamics does not stop even in the extreme limit of subdiffusion. Surprisingly, this small difference leads to large consequences. The main results we report here are exact results showing ultraslow diffusion and a stationary diffusion regime (i.e., localization). Specifically, the equations of motion are solved analytically for the first two moments, allowing the determination of the Hurst exponent. Several anomalous diffusion regimes are apparent, ranging from superdiffusion to subdiffusion, as well as ultraslow and stationary regimes. We present the complete phase diffusion diagram, along with a study of the persistence and the statistics in the regions of interest.