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
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.
2017, Vol. 34 
