Qualitative Features at the Glass Crossover

Abstract

We discuss some generic features of the dynamics of glass-forming liquids close to the glass transition singularity of the idealized mode-coupling theory (MCT). The analysis is based on a recent model by one of the authors for the intermediate-time dynamics ($\beta$ relaxation), derived by applying dynamical field-theory techniques to the idealized MCT. Combined with the assumption of time-temperature superposition for the slow structural ($\alpha$) relaxation, the model naturally explains three prominent features of the dynamical crossover: the change from a power-law to exponential increase in the structural relaxation time, the replacement of the Stokes-Einstein relation between diffusion and viscosity by a fractional law, and two distinct growth regimes of the thermal susceptibility that has been associated to dynamical heterogeneities.