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We consider the problem of slow activation dynamics in glassy systemsundergoing a random first order phase transition. Using an effective potentialapproach to supercooled liquids, we determine the spectrum of activationbarriers for entropic droplets. We demonstrate that fluctuations of theconfigurational entropy and of the liquid glass surface tension are crucial toachieve an understanding of the barrier fluctuations in glassy systems and thusare ultimatively responsible for the broad spectrum of excitations andheterogeneous dynamics in glasses. In particular we derive a relation betweenthe length scale for dynamic heterogeneity and the related barrierfluctuations. Diluted entropic droplets are shown to have a Gaussiandistribution of barriers, strongly suggesting that non-Gaussian behaviorresults from droplet-droplet interactions.

Replica theory for fluctuations of the activation barriers in glassy systems