Relaxation Rate Distributions for Supercooled Liquids

The mode-coupling theory for the evolution of glassy dynamics in simple liquids yields correlation functions that, outside the transient regime, can be written as a superposition of relaxators with a broad distribution of relaxation rates. The known asymptotic laws for the dynamics near an ideal glass transition imply corresponding laws for the rate distribution. We calculate the rate distributions for a hard-sphere liquid and compare them to the leading and next-to-leading asymptotic formulas.