Further Simplifying the Glass Problem
The random Lorentz gas (RLG) is a minimal model of both transport in heterogenous media and structural glasses. Yet these two perspectives are fundamentally inconsistent, as the dynamical arrest is continuous in the former and discontinuous in the latter. This tension hinders our understanding of either phenomenon, as well as of the RLG itself. By considering an exact solution of the RLG in the infinite- dimensional d ? ? limit as well as numerics in d = 2 . . . 20 we here resolve this paradox. Our results reveal the importance of instantonic corrections, related to rare cage escapes, in unifying glass and percolation physics. This advance suggests a starting point for a first-principle description of hopping processes in structural glasses. We also conjecture tighter formal bounds on the asymptotic d ? ? RLG percolation threshold, which may further enlighten our understanding of that model.