Generalized Master Equation for Space-Time Coupled Continuous Time Random Walk

【摘要】 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）^tγ,0≤γ< 2, and the probability density function ω（t） of a particle’s waiting time t follows a power law form for large t: ω（t）^t-（1+α）,0 <α< 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent γ and the long-tailed index α 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.更多还原

【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）^tγ,0≤γ< 2, and the probability density function ω（t） of a particle’s waiting time t follows a power law form for large t: ω（t）^t-（1+α）,0 <α< 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent γ and the long-tailed index α 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.更多还原