Relaxation Time Spectrum in Glassy States

Pik-Yin Lai

Chinese Journal of Physics

33卷3期（1995 / 06 / 01）

271 - 277

英文

The spectrum for the distribution of the relaxation times that leads to the universally observed Kohlraush law, or stretched exponential relaxation exp(-(t/τ0)α) (0 ＜ α ＜ l), for the time correlation function in glassy systems, is calculated. For a = 1/2, we obtain explicitly the distribution of the relaxation spectrum. For general values of a, all the moments of the distribution are computed explicitly. We find that for α ＜ 1 the distribution has a broad spectrum with the width of the distribution and the average relaxation time diverges over tens of orders of magnitude as α becomes close to 0. The plausible connections with the Vogel-Fulcher and Arrhenius laws are also discussed.