Models of traps and glass phenomenology

Abstract

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.

35 pages, 2 figures (not included). The two figures are available upon request

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