Role of Unstable Directions in the Equilibrium and Aging Dynamics of Supercooled Liquids

The connectivity of the potential energy landscape in supercooled atomic liquids is investigated through a calculation of the instantaneous normal modes spectrum and a detailed analysis of the unstable directions in configuration space. We confirm the hypothesis that the mode-coupling critical temperature is the $T$ at which the dynamics crosses over from free to activated exploration of configuration space. We also observe changes in the local connectivity of configuration space sampled during aging, following a temperature jump from a liquid to a glassy state.