CONTINUOUS-TIME RANDOM-WALK MODEL AS A MODEL OF ANOMALOUS RELAXATION

The microscopic models of anomalous structural relaxation are proposed and studied within the framework of the continuous time random walk. The Cole-Cole type relaxation is observed in the model with the fracta l nature where the waiting time distribution, psi(t), of the random wa lker is given by the power-law, psi(t) alpha h(-1-a), with a < 1. The relaxation also becomes of the Cole-Cole type even when we introduce t he correlation between the direction of two successive jumps, suggesti ng the robustness of this property. On the other hand, the stretched-e xponential type relaxation appears when the fractal nature of the mode l is removed by the upper cutoff of the waiting time. These results sh ow that the type of the relaxation is strongly related to the (non-) f ractal nature of the system.