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How useful it is to think about the potential energy landscape of a complexmany-body system depends in large measure on how direct the connection is tothe system's dynamics. In this paper we show that, within what we call thepotential energy landscape ensemble, it is possible to make direct connectionsbetween the geometry of the landscape and the long-time dynamical behaviors ofsystems such as supercooled liquids. We show, in particular, that the onset ofslow dynamics in such systems is governed directly by the lengths of theirgeodesics - the shortest paths through their landscapes within the specialensemble. The more convoluted and labyrinthine these geodesics are, the slowerthat dynamics is. Geodesics in the landscape ensemble have sufficientlywell-defined characteristics that is straightforward to search for themnumerically, a point we illustrate by computing the geodesic lengths for anordinary atomic liquid and a binary glass-forming atomic mixture. We find thatthe temperature dependence of the diffusion constants of these systems,including the precipitous drop as the glass-forming system approaches itsmode-coupling transition, is predicted quantitatively by the growth of thegeodesic path lengths.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Global perspectives on the energy landscapes of liquids, supercooled  liquids, and glassy systems: Geodesic pathways through the potential energy  landscape