College of Sciences, Nanjing Agricultural University, Nanjing 210095, People's Republic of China.
School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China.
Chaos. 2023 Jan;33(1):013102. doi: 10.1063/5.0124654.
Aging phenomena have been observed in numerous physical systems. Many statistical quantities depend on the aging time t 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 the Lévy walk and the generalized Green-Kubo formula, we investigate the quantities that include the ensemble- and time-averaged mean-squared displacements in both weak aging t≪t and strong aging t≫t cases and compare them to the ones in the absence of any force field. Two typical force fields, constant force F and time-dependent periodic force F(t)=fsin(ωt), are considered for comparison. The generalized Einstein relation is also discussed in the case with the constant force. We find that the constant force is the key to causing the aging phenomena and enhancing the diffusion behavior of the aging Lévy walk, while the time-dependent periodic force is not. The different effects of the two kinds of forces on the aging Lévy walk are verified by both theoretical analyses and numerical simulations.
老化现象在众多物理系统中都有观察到。对于老化的异常扩散过程，许多统计量都依赖于老化时间 t。本文更关注外力场如何影响老化 Lévy 漫步。基于 Lévy 漫步的 Langevin 图像和广义 Green-Kubo 公式，我们研究了包括在弱老化 t≪t 和强老化 t≫t 情况下的系综平均和时间平均均方位移的量，并将它们与没有任何力场的情况下进行了比较。为了进行比较，我们考虑了两种典型的力场，即恒力 F 和时变周期性力 F(t)=fsin(ωt)。在存在恒力的情况下，还讨论了广义爱因斯坦关系。我们发现，恒力是导致老化现象和增强老化 Lévy 漫步扩散行为的关键，而时变周期性力则不是。这两种力对老化 Lévy 漫步的不同影响通过理论分析和数值模拟得到了验证。
