Non-Perturbative Processes in Glasses

This chapter reviews non-perturbative processes in glasses, which play an extremely important role in their dynamics. In a first contribution (Sec. 8.1), P. Wolynes shows how the Random First Order Transition theory of glasses can take into account spatial and temporal fluctuations, via a variety of non-perturbative instantonic processes. This description is applied to the study of the supercooled liquid dynamics in the vicinity of the glass transition, but also to the plasticity and yielding of the amorphous solid. In a second contribution (Sec. 8.2), T. Rizzo reviews a systematic expansion around dynamical mean field theory, that can be used to study how the mode-coupling dynamical arrest is avoided in finite-dimensional glasses. A stochastic beta-relaxation equation is derived, and used to describe the crossover from diffusive to activated dynamics of the supercooled liquid. The approach is demonstrated for the paradigmatic Ising p-spin glass model, by comparing theoretical predictions and numerical simulation data