Qualitative features at the glass crossover

Abstract

We discuss 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 theory by one of the authors for the intermediate-time dynamics ($\beta$ relaxation), derived by applying dynamical field-theory techniques to the idealized MCT. Taking the long-time asymptote of the $\beta$-relaxation regime as a proxy for universal aspects of the slow structural ($\alpha$) relaxation, we explain 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.