On The Nature of the Glass Crossover

Abstract: Stochastic Beta Relaxation (SBR) is a model for the dynamics of glass- forming liquids close to the glass transition singularity of the idealized mode- coupling theory (MCT) that has been derived from generic MCT-like theories by applying dynamical field-theory techniques. SBR displays a rich phenomenology common to most super-cooled liquids. In its simplest version it naturally explains two prominent features of the dynamical crossover: the change from a power-law to exponential increase in the structural relaxation time and the violation of the Stokes-Einstein relation between diffusion and viscosity. The solution of the model in three dimensions unveils a qualitative change at the crossover in the structure of dynamical fluctuations from a regime characterized by power-law increases of their amplitude and size to a regime dominated by strong Dynamical Heterogeneities: rare regions where dynamics is relatively much faster than in the rest of the system. While the relaxation time changes by orders of magnitude, the size of these regions does not change significantly and actually decreases below the crossover temperature. SBR cannot sustain too large fluctuations and could fail well below the crossover temperature. There it could be replaced by non-conventional activated dynamics characterized by elementary events with intrinsic time and length scales of an unusual large (but not necessarily increasing) size (mesoscopic vs. microscopic).