| GENERAL |
|
|
|
|
Generalized Master Equation for Space-Time Coupled Continuous Time Random Walk |
| Jian Liu1,2**, Bao-He Li1, Xiao-Song Chen2 |
1School of Science, Beijing Technology and Business University, Beijing, 100048
2CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190
|
|
| Cite this article: |
|
Jian Liu, Bao-He Li, Xiao-Song Chen 2017 Chin. Phys. Lett. 34 050201 |
|
|
|
|
Abstract The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function $g(t) \sim t^{\gamma}$, $0 \le \gamma < 2$, and the probability density function $\omega(t)$ of a particle's waiting time $t$ follows a power law form for large $t$: $\omega(t) \sim t^{-(1+\alpha)}$, $0 < \alpha < 1$. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent $\gamma$ and the long-tailed index $\alpha$ of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.
|
| Keywords:
|
|
|
Received: 06 March 2017
Published: 29 April 2017
|
|
| PACS: |
02.50.Ey
|
(Stochastic processes)
|
| |
05.40.Fb
|
(Random walks and Levy flights)
|
| |
02.60.Cb
|
(Numerical simulation; solution of equations)
|
|
|
| Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11605003 and 11547231. |
|
|
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
