Abstract

In several physical systems the experimental thermal decay from an initial metastable state to a final stable state is frequently logarithmic over a few decades in time. The quantity plotted is the probability of not reaching the final stable state, or an equivalent variable. Logarithmic slopes locally higher than In(10)/e ? 0.85 are shown to rule out two frequent explanations for these processes: thermal activation over a single barrier with Arrhenius exponential decay, or decay through parallel processes of Arrhenius type occurring at different rates. We present a model of thermal decay that can show these high logarithmic decay rates or fast relaxation, as here defined. A downward cascade of metastable states is assumed between the initial and final states, and the evolution of the probability distribution is described by a Master equation. 'Fast' relaxation is obtained for consecutive states separated by equal direct and equal reverse barriers, the latter being much higher. These solutions correspond to almost degenerate decay rates, and to low relative dispersion of switching times. The results of this model may explain measurements of 'fast' thermal relaxation of the magnetization of single magnetic particles near the coercive field.