Spectral characterization of aging: the rem-like trap model

Details Spectral characterization of aging: the rem-like trap model Spectral characterization of aging: the rem-like trap model

2005-08-25

arxiv.org/abs/math/0508486v1

Annals of Applied Probability 2005, Vol. 15, No. 3, 1997-2037

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000359 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000359

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. 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 analyze the dynamics on various time scales.

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