LACK OF EQUILIBRATION IN A MODEL FOR CONTINUOUSLY SUPERCOOLED LIQUIDS

We consider the dynamics of supercooled fluids subject to a continuous quenching procedure, with cooling rate r = dT(t)/dt. The analysis is carried out analytically in the framework of a mean field schematic model recently introduced.1 We show the existence of a glass temperature Tg(r) below which the system falls out of equilibrium. Tg(r) approaches logarithmically in r the ideal glass temperature T0 = lim r→0Tg(r), where the relaxation time diverges á la Vogel-Fulcher, similarly to some experimental observations. Well above Tg(r) a simple fluid behavior is observed. As Tg is approached from above a characteristic wave vector kd divides an high momenta equilibrated region, where a fluid-like behavior is obeyed, from the non thermalized modes with k < kd, for which time translational invariance lacks. Below Tg the system is found in a globally off-equilibrium glassy state characterized by a logarithmic decay of the density fluctuations and aging. The two time correlator decays as an enhanced power law.