Time correlation functions between Inherent Structures: a connection between landscape topology and the dynamics of glassy systems

We introduce time correlation functions between Inherent Structures (IS) of a supercooled liquid. We show that these functions are useful to relate the slowing down of the dynamics to the structure of the energy landscape near the glass transition temperature. They show a short time regime during which the system remains in the basin of a particular IS and a long time regime where it explores the neighborhood of an IS. We compare the behavior of these functions in a binary Lennard-Jones supercooled liquid and in a model of traps and show that they behave qualitatively different. This comparison reflects the presence/absence of structure in the landscape of the Lennard-Jones/traps models. Possible scenarios for the structure of the landscape which are compatible with these results are discussed.