Reaction Dynamics of Continuous Time Random Walker in Heterogeneous Environment

초록

We report an exact relation between the survival probability, the revisit time distribution, and the reaction-free propagator of the continuous time random walker. The relation holds even for such a general case where the random walker has a distinct jump dynamics at each lattice site, which may be dependent also on the direction of the jump. The application range of the obtainedrelation is not limited to the nearest neighbor hopping in the bulk lattice either. The result is applicable to a higher dimensional system with the spherical symmetry as well as it is to the one-dimensional system.