Irreducible memory function and slow dynamics in disordered systems

We show how the irreducible memory function can be obtained in a rather straightforward way, and that it can be expressed in terms of two contributions representing two parallel decay channels. This representation should be useful for treating systems with a slow time dependence and where eventually some internal degrees of freedom enters in the relaxation process, and cuts off an underlying ideal ergodic to nonergodic transition. We also show how the irreducible memory function under certain mild conditions defines a regenerative stochastic process, or a two level stochastic system. This leads to a picture with dynamical heterogeneities, where the statistical properties asymptotically are ruled by limit processes. This can explain the universal behavior observed in many glass-forming systems.