The heterogeneous energy landscape expression of KWW relaxation

Here we show a heterogeneous energy landscape approach to describing the Kohlrausch-Williams-Watts (KWW) relaxation function. For a homogeneous dynamic process, the distribution of free energy landscape is first proposed, revealing the significance of rugged fluctuations. In view of the heterogeneous relaxation given in two dynamic phases and the transmission coefficient in a rate process, we obtain a general characteristic relaxation time distribution equation for the KWW function in a closed, analytic form. Analyses of numerical computation show excellent accuracy, both in time and frequency domains, in the convergent performance of the heterogeneous energy landscape expression and shunning the catastrophic truncations reported in the previous work. The stretched exponential β, closely associated to temperature and apparent correlation with one dynamic phase, reveals a threshold value of 1/2 defining different behavior of the probability density functions. Our work may contribute, for example, to in-depth comprehension of the dynamic mechanism of glass transition, which cannot be provided by existing approaches.