  We review the ageing phenomenon in the context of 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 diagonalised exactly.
Using this result, we derive closed expressions for correlation functions 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 context we analyse the dynamics on various time
scales.
