Microscopic derivation of jump rate distribution and the glass transition

A general framework is given for deriving the jump rate distribution functi on and the long-time behaviour of the waiting time distribution for the jum p is shown to be a power-law function whose exponent is related to the cont ribution of fast modes relative to that of slow modes in the density fluctu ation. A unified explanation for the vitrification process and glass transi tion singularities is presented.