Dynamics of the Random Potential Spherical Model

– The dynamics of many continuous degrees of freedom interacting via a random potential and subject to a global spherical constraint is investigated. The model is a prototype mean-field model for structural glasses near the glass transition. In the high temperature phase the model is described by equations similar to those of the Schematic Mode Coupling Theory for structural glasses. The analysis of the nonlinearities of the potential reveals three different scenarios for the critical dynamics. In particular the presence of both local stress and cubic non-linearities leads to a critical dynamics typical of structural flagile glasses. For each scenario we introduce a " minimal " model representative of the critical dynamics. In the last years many efforts have been devoted to study the relaxation dynamics of undercooled liquids near the (structural) glass transition. When the temperature of the liquid is lowered down to the critical glass temperature relaxation times becomes exceedingly long and diffusional degrees of freedom freeze over very long time scales. As a consequence the difference between a structural glass and a disordered system with quenched disorder, which may seem essential, becomes less and less sharp as the transition is approached since the particles in the liquid become trapped in random postition (cage effect) and the dynamics of a single degrees of freedom resembles the relaxational dynamics in a random quenched potential. The idea that a undercooled liquid is a sort of random solid, which dates back to Maxwell [1], has been recently largely used in the study of the glass transition in undercooled liquids. In this scenario is, for example, the study of the Instantaneous Normal Mode (INM) [2], where the N-body potential is analyzed in terms of normal modes of oscillations about a given istantaneous configuration.