Cooperative transitions in the random energy model for supercooled liquids

In the usual random energy model for supercooled liquids, the particles can occupy traps of various depths E, which they can leave by thermal excitation. An extension of this model is considered in which the particles can leave the traps by two possible routes, corresponding to direct thermal excitation of single particles to the energy E = 0 and to the correlated motion of a group of particles with a lower activation energy and smaller prefactor. In the model studied here, the traps for the particles are grouped into sets with discrete depths E_j and with two different sets of densities g(E_j). Our calculations show that, as the temperature is lowered, the second mechanism starts to dominate the system's dynamics, and that with the appropriate densities of states the combined mechanism can lead to meaningful results.