Different effects of external force fields on aging Lévy walk

Author:

Chen Yao1ORCID,Wang Xudong2ORCID

Affiliation:

1. College of Sciences, Nanjing Agricultural University 1 , Nanjing 210095, People’s Republic of China

2. School of Mathematics and Statistics, Nanjing University of Science and Technology 2 , Nanjing 210094, People’s Republic of China

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 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 ta≪t and strong aging ta≫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)=f0sin⁡(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.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Jiangsu Province

Publisher

AIP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

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