Macroscopic finite size effects in relaxational processes
We present results on dynamical processes that exhibit a stretched exponential relaxation. When the relaxation is a result of two competing exponential processes, the size of the system, although macroscopic, play a dominant role. There exist a crossover time t x that depends logarithmically on the size of the system, above which, the relaxation changes from a stretched exponential to a simple exponential decay. The decay rate also depends logarithmically on the size of the system. These results are relevant to large-scale Monte-Carlo simulations and should be amenable to experiments in low-dimensional macroscopic systems and mesoscopic systems.
KeywordsRelaxational Process System Size Relaxation Function Finite System Macroscopic System
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