%0 Journal Article %T Microscopic Theory of Heterogeneity and Non-Exponential Relaxations in Supercooled Liquids %A Xiaoyu Xia %A Peter G. Wolynes %J Physics %D 2000 %I arXiv %R 10.1103/PhysRevLett.86.5526 %X 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. %U http://arxiv.org/abs/cond-mat/0008432v1