Linear and nonlinear response in the aging regime of the one-dimensional trap model

We investigate the behavior of the response function in the one-dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time [Formula presented] given that a small bias h is applied at time [Formula presented] Several scaling regimes are found, depending on the relative values of [Formula presented] [Formula presented] and [Formula presented] Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation-dissipation relation is valid even in the aging regime, at least for times such that linear response is obeyed. However, for sufficiently long times, the response always becomes nonlinear in [Formula presented]. © 2003 The American Physical Society.