论文标题
外力场对老化lévy步行的不同影响
Different effects of external force fields on aging Lévy walk
论文作者
论文摘要
在许多物理系统中已经观察到衰老现象。许多统计量取决于老化异常扩散过程的老化时间$ t_a $。本文更加关注外力场如何影响老化的莱维步行。根据LévyWalk的Langevin图片和广义绿色Kubo公式，我们研究了数量，其中包括弱老化的$ T_A \ ll T $和强大的老化$ T_A \ gg T $中的合奏和时间平均的于点的位移，并将其与数量相比，在没有任何力量的情况下将它们与数量进行比较。考虑比较两个典型的力场，即恒定力$ f $和时间依赖的周期性$ f（t）= f_0 \ sin（ωt）$。在恒定力的情况下，还讨论了广义的爱因斯坦关系。我们发现，恒定力是产生衰老现象并增强衰老lévy步行的扩散行为的关键，而时间依赖的周期性不是。通过理论分析和数值模拟验证了两种力对LévyWalk衰老现象的不同影响。
Aging phenomena have been observed in numerous physical systems. Many statistical quantities depend on the aging time $t_a$ for aging anomalous diffusion processes. This paper pays more attention to how an external force field affects the aging Lévy walk. Based on the Langevin picture of Lévy walk and generalized Green-Kubo formula, we investigate the quantities which include the ensemble- and time-averaged mean-squared displacements in both weak aging $t_a\ll t$ and strong aging $t_a\gg t$ cases, and compare them to the quantities in the absence of any force field. Two typical force fields, constant force $F$ and time-dependent periodic force $F(t)=f_0\sin(ωt)$, are considered for comparison. The generalized Einstein relation is also discussed in the case with constant force. We find that the constant force is the key of generating the aging phenomena and enhancing the diffusion behavior of aging Lévy walk, while the time-dependent periodic force is not. The different effects of the two kinds of forces on the aging phenomena of Lévy walk are verified by both theoretical analyses and numerical simulations.
