Abstract
In this paper we give the results of our recent work on thedynamical TAP (Thouless-Anderson-Palmer) approach to mean-fieldglassy systems. Our aim is to clarify the connection between thefree-energy landscape and the out-of-equilibrium dynamics insolvable models.Frequently, qualitative explanations of glassy behaviour are basedon the `free-energy landscape paradigm'. While its relevance forequilibrium properties may be clear, the relationship between thefree-energy landscape and out-of-equilibrium dynamics is not wellunderstood yet. In this paper we clarify this relationship for theclass of spin-glass models which reproduce phenomenologically somefeatures of structural glasses. The method that we use is ageneralization of the dynamics of the Thouless, Anderson and Palmerapproach to the thermodynamics of mean-field spin glasses. Withinthis framework, we show to what extent the dynamics can berepresented as an evolution in the free-energy landscape. Inparticular, the relationship between the long-time dynamics and thelocal properties of the free-energy landscape is explicitly apparentusing this approach.
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