Abstract
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.
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Havlin, S., Bunde, A., Klafter, J. (1999). Macroscopic finite size effects in relaxational processes. In: Pękalski, A., Sznajd-Weron, K. (eds) Anomalous Diffusion From Basics to Applications. Lecture Notes in Physics, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106839
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DOI: https://doi.org/10.1007/BFb0106839
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