Dependence of supercooled liquid dynamics on elevation in the energy landscape

Quenches of the Lennard-Jones unit density, $N=256$ supercooled liquid are analyzed to show that the activation energy for diffusion, Eₐ, increases as the energy of the associated local minimum on the potential energy landscape, Uₘ, decreases. Super-Arrhenius T dependence of the self-diffusion constant D, characteristic of fragile liquids, is thus a consequence of the descent of the system, with decreasing T, from a plateau of Uₘ values at the top of the landscape. Departure from the top occurs at a random temperature Tₛ but introduction of Eₐ(Uₘ) allows a systematic analysis of $D(T).$ A single quench exhibits several features of the experimental glass transition. Fast cooling in prior work has isolated the supercooled ``top'' state only. The difference between strong and fragile liquids, and the fate of the quenches, is discussed in terms of the landscape and its N dependence.