Time correlation functions between inherent structures: a connection between landscape topology and the dynamics of glassy systems

In this work 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 neighbourhood of an IS. We compare the behaviour of these functions in a binary Lennard-Jones glass 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