  Dynamic facilitation theory assumes short-ranged dynamic constraints to be
the essential feature of supercooled liquids and draws much of its conclusions
from the study of kinetically constrained models. While deceptively simple,
these models predict the existence of trajectories that maintain a high overlap
with their initial state over many structural relaxation times. We use
molecular dynamics simulations combined with importance sampling in trajectory
space to test this prediction through counting long-lived particle
displacements. For observation times longer than the structural relaxation time
exponential tails emerge in the probability distribution of this number.
Reweighting trajectories towards low mobility corresponds to a phase transition
into an inactive phase. While dynamics in these two phases is drastically
different structural measures show only slight differences. We discuss the
choice of dynamic order parameter and give a possible explanation for the
microscopic origin of the effective dynamic constraints.
