Eur. Phys. J. B (2015) 88: 88
https://doi.org/10.1140/epjb/e2015-60056-y

Regular Article

Dynamical continuous time random walk

¹ State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
² Kavli Institute for Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
³ Department of Physics, Beijing Normal University, Beijing 100875, P.R. China

^a e-mail: liujian@mail.bnu.edu.cn

Received: 19 January 2015
Received in final form: 3 March 2015
Published online: 6 April 2015

Abstract

We consider a continuous time random walk model in which each jump is considered to be dynamical process. Dissipative launch velocity and hopping time in each jump is the key factor in this model. Within the model, normal diffusion and anomalous diffusion is realized theoretically and numerically in the force free potential. Besides, external potential can be introduced naturally, so the random walker’s behavior in the linear potential and quartic potential is discussed, especially the walker with Lévy velocity in the quartic potential, bimodal behavior of the spatial distribution is observed, it is shown that due to the inertial effect induced by damping term, there exists transition from unimodality to bimodality for the walker’s spatial stationary distribution.