Models of traps and glass phenomenology

We study various models of independent particles hopping between energy 'traps' with a density of energy barriers rho(E), on a d-dimensional lattice or on a fully connected lattice. If rho(E) decays exponentially, a true dynamical phase transition between a high-temperature 'liquid' phase and a low-temperature 'aging' phase occurs. More generally, however, one expects that for a large class of rho(E),'interrupted' aging effects appear at low enough temperatures, with an ergodic time growing faster than exponentially. The relaxation functions exhibit a characteristic shoulder, which can be fitted as stretched exponentials. A simple way of introducing interactions between the particles leads to a modified model with an effective diffusion constant in energy space, which we discuss in detail.