The role of the free-energy landscape in the dynamics of mean-field glassy systems

In this paper we give the results of our recent work on the dynamical TAP (Thouless-Anderson-Palmer) approach to mean-field glassy systems. Our aim is to clarify the connection between the free-energy landscape and the out-of-equilibrium dynamics in solvable models. Frequently, qualitative explanations of glassy behaviour are based on the 'free-energy landscape paradigm'. While its relevance for equilibrium properties may be clear, the relationship between the free-energy landscape and out-of-equilibrium dynamics is not well understood yet. In this paper we clarify this relationship for the class of spin-glass models which reproduce phenomenologically some features of structural glasses. The method that we use is a generalization of the dynamics of the Thouless, Anderson and Palmer approach to the thermodynamics of mean-field spin glasses. Within this framework, we show to what extent the dynamics can be represented as an evolution in the free-energy landscape. In particular, the relationship between the long-time dynamics and the local properties of the free-energy landscape is explicitly apparent using this approach.