RELAXATION-TIME SPECTRUM IN GLASSY STATES

The spectrum for the distribution of the relaxation times that leads t o the universally observed Kohlraush law, or stretched exponential rel axation exp(-(t/tau(0))(alpha)) (0 < alpha < 1), for the time correlat ion function in glassy systems, is calculated. For alpha = 1/2, we obt ain explicitly the distribution of the relaxation spectrum. For genera l values of ct, all the moments of the distribution are computed expli citly. We find that for alpha < 1 the distribution has a broad spectru m with the width of the distribution and the average relaxation time d iverges over tens of orders of magnitude as alpha becomes close to 0. The plausible connections with the Vogel-Fulcher and Arrhenius laws ar e also discussed.