Role of unstable directions in the equilibrium and aging dynamics of supercooled liquids

The connectivity of the potential energy landscape in supercooled atomic li quids is investigated through a calculation of the instantaneous normal mod es spectrum and a detailed analysis of the unstable directions in configura tion space. We confirm the hypothesis that the mode-coupling critical tempe rature is the T at which the dynamics crosses over from free to activated e xploration of configuration space. We also observe changes in the local con nectivity of configuration space sampled during aging, following a temperat ure jump from a liquid to a glassy state.