Spectral characterization of ageing: the REM-like trap model.

We review the aging phenomenon in the context of the simplest trap model, Bouchaud's REM-like trap model, from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalized exactly. Usingt his result, we derive c losed expressions for correlation fu nctions in terms of complex contour integrals that permit an easy investigation into their large time asymptotics in the thermodynamic limit. We also give a grand canonical representation of the model in terms of the Markov process on a Poisson point process. In this contest we analyze the dynamics on various time scales.