Incorporating activated hopping processes into the mode-coupling theory for glassy dynamics

A new attempt for extending the idealized mode-coupling theory (MCT) for glass transition is presented which incorporates activated hopping processes via the dynamical theory originally developed to describe diffusion-jump processes in crystals. The approach adapted here to glass-forming liquids treats hopping as arising from vibrational fluctuations in quasi-arrested state where particles are trapped inside their cages, and the hopping rate is formulated in terms of the Debye-Waller factor characterizing the structure of the quasi-arrested state. The resulting expression for the hopping rate takes an activated form, in which the barrier height is "self-generated" in the sense that it is present only in those supercooled states where the dynamics exhibits a well defined plateau. It is discussed how such a hopping rate can be incorporated into MCT so that the sharp nonergodic transition predicted by the idealized version of the theory is replaced by a rapid but smooth crossover. Preliminary result for the hard-sphere system is also presented.