Dynamical caging and activation in random Lorentz gas model*

Mean-field theory predicts that a dynamical (or mode-coupling) transition leads to particle caging and hence glass formation. In finite-dimensional systems, however, this transition is avoided due to activated processes and other effects. Obtaining a first-principle description of these effects remains one of the most challenging aspects of the glass problem. We here study these effects in the random Lorentz gas (RLG). This minimal model indeed shares a same mean-field description with structural glasses, but only allows certain instantonic corrections to proceed. The vicinity of the dynamical transition can then be carefully examined. The systematic comparison between theoretical descriptions and high-d simulations reveals both qualitative and quantitative corrections to the mean-field behavior. In the caging regime, we have thus identified two types of finite-d corrections: perturbative corrections to the cage size and non-perturbative cage escapes. In the diffusing regime, we further identified a microscopic origin of the Stokes-Einstein relation breakdown. Our results thereby provide strong guidelines for a theory of activation, and offer a first-principle pathway for relating local structure and dynamics in glass-forming liquids.