Void Percolation Threshold and Critical Proporties of the Random Lorentz Gas

Percolation and glass formation share interesting dynamical features, in which they both exhibit caging of tracers/particles. Although first noticed long ago, this analogy has grown in physical relevance since a simplified model of structural glasses (Mari-Kurchan) was found to display corrections to caging that are analogous to those observed in percolating systems. Interestingly, our recent study has shown that the glass-like caging transition is absent in lattice percolation for all dimensions. In order to better understand the origin of caging, we consider transport in an off-lattice percolation model. Specifically, we study the caging and critical scaling of transport in the random Lorentz gas, which can be mapped onto the Mari-Kurchan model and to void percolation. We first develop numerical strategies to determine precisely the void percolation threshold in high dimensions, and then study dynamical criticality around that threshold. Our results provide key insights into the dynamics of glass formers and transport in heterogenous media, more generally.