Different effects of external force fields on aging L\'evy walk
Abstract
Aging phenomena have been observed in numerous physical systems. Many statistical quantities depend on the aging time ta for aging anomalous diffusion processes. This paper pays more attention to how an external force field affects the aging L\'evy walk. Based on the Langevin picture of L\'evy walk and generalized Green-Kubo formula, we investigate the quantities which include the ensemble- and time-averaged mean-squared displacements in both weak aging ta t and strong aging ta 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)=f0(ω t), 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 L\'evy walk, while the time-dependent periodic force is not. The different effects of the two kinds of forces on the aging phenomena of L\'evy walk are verified by both theoretical analyses and numerical simulations.
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