Microscopic Theory of Heterogeneity and Non-Exponential Relaxations in Supercooled Liquids

Recent experiments and computer simulations show that supercooled liquids around the glass transition temperature are "dynamically heterogeneous" [1]. Such heterogeneity is expected from the random first order transition theory of the glass transition. Using a microscopic approach based on this theory, we derive a relation between the departure from Debye relaxation as characterized by the $\beta$ value of a stretched exponential response function $\phi(t) =e^{-(t/ \tau_{KWW})^{\beta}}$, and the fragility of the liquid. The $\beta$ value is also predicted to depend on temperature and to vanish as the ideal glass transition is approached at the Kauzmann temperature.