  A complete understanding of the precipitous onset of slow dynamics in systems
such as supercooled liquids requires making direct connections between dynamics
and the underlying potential energy landscape. With the aid of a switch in
ensembles, we show that it is possible to formulate a landscape-based mechanism
for the onset of slow dynamics based on the rapid lengthening of the geodesic
paths that traverse the landscape. We confirm the usefulness of this purely
geometric analysis by showing that it successfully predicts the diffusion
constants of a standard model supercooled liquid.
