Effect of different waiting time processes with memory to anomalous diffusion dynamics in an external force fields
Effect of different waiting time processes with memory to anomalous diffusion dynamics in an external force fields
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不同记忆等待时间过程对外力场中异常扩散动力学的影响
DOI：
10.1016/j.physa.2014.09.040
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发表时间：
2015
影响因子：
3.3
通讯作者：
Qiu Wei-Yuan
中科院分区：
文献类型：
--
作者：
Ren Fu-Yao;Wang Jun;Lv Long-Jin;Pan Hua;Qiu Wei-Yuan
本文研究了粒子在外力场中的反常扩散，它的运动由无更新的带记忆的连续时间随机游动控制。在我们的模型中，等待时间涉及Riemann-Liouville分数阶导数或Riemann-Liouville分数阶积分。得到了系统的均方位移观测、Fokker-Planck型动力学方程及其定态解。这些过程遵循广义的爱因斯坦-斯托克斯-斯莫卢乔夫斯基关系，并遵守第二爱因斯坦关系。等待时间和隶属度的渐近行为服从加长的高斯分布。我们还讨论了在外力场的情况下的平均时间，并表明这个过程表现出老化和遍历破裂。
In this paper, we study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with memory. In our models, the waiting time involves Riemann–Liouville fractional derivative or Riemann–Liouville fractional integral. We obtain the systematic observation on the mean squared displacement, the Fokker–Planck-type dynamic equations and their stationary solutions. These processes obey a generalized Einstein–Stokes–Smoluchowski relation, and observe the second Einstein relation. The asymptotic behavior of waiting times and subordinations are of stretched Gaussian distributions. We also discuss the time averaged in the case of an external force field, and show that the process exhibits aging and ergodicity breaking.