In my graduate studies I worked with a simplified version of mode-coupling theory (MCT), which, for all its flaws, attempts to operate at a truly predictive, microscopic, force-level description, and which nonlinearly couples liquid relaxation to collective pair-density fluctuations to try to explain glassy dynamics. After invoking uncontrolled projection and dynamic Gaussian (factorization) approximations, the collective and self dynamic structure factors can be computed using only the equilibrium pair structure as input. Despite the very modest changes in equilibrium pair structure as the glass transition is crossed, MCT has a highly nonlinear feedback mechanism that greatly amplifies these small changes in structure, resulting in a divergent dynamical slowing down of the system.
Ideal MCT has had considerable success in the dynamic “precursor” or “crossover” regime in which the relaxation slows down by only a few orders of magnitude. However, the use of a particular uncontrolled approximation, essentially the factorization of a four-point correlator into a product of two-point correlators (a dynamic Gaussian approximation), results in a spurious non-ergodicity transition at a relatively high temperature in viscous liquids (or low volume fraction in particle suspensions). In reality, ergodicity is restored via highly non-Gaussian activated barrier hopping events. My work built upon work by Saltzman and Schweizer, which included single-particle hopping events in a simplified MCT framework, to include correlated two-particle activated events.