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Dynamical TAP approach to mean field glassy systems. (English) Zbl 0955.82031

Summary: The Thouless, Anderson and Palmer (TAP) approach to thermodynamics of mean field spin glasses is generalized to dynamics. A method to compute the dynamical TAP equations is developed and applied to the \(p\)-spin spherical model. In this context 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 shows up explicitly within this approach. Conversely, by an instantaneous normal modes analysis we show that the local properties of the energy landscape seen by the system during its dynamical evolution do not change qualitatively at the dynamical transition.

MSC:

82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
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